I'm not sure why attention in exercise questions is always focused on soldiers.

While I can't show you a Stronglifts VxV, there's plenty of evidence that medieval people engaged in sports-type activities for fun. But sources also indicate the awareness that regular physical activity was good for someone's health, not just their emotional well-being.

In the early fifteenth century, for example, French humanist and all-around awesome Christine de Pizan wrote a book of advice for women, The Treasure of the City of Ladies:

...If it is summer, she will go off to amuse herself in a garden until supper-time, walking up and down for her health.

(trans. Sarah Lawson)

This is prescriptive, not descriptive, it's true. But in the context of Treasure, the advice needed to come across as realistic to its readers. So the idea of walking for health was indeed in circulation.

(In the 16th century, we can see this in descriptive sources for Jeanne de Navarre, at least.)

As for men, our most excellent prescriptive source is an exemplar "letter"--probably an instructive text for early university students:

If you will, walk daily somewhere morning and evening. ANd if the weather is cold, if you can run, run on an empty stomach, or at least walk rapidly, that the natural heat may be revived. However, it is not advisable to run on a full stomach but to saunter slowly...

...If you cannot go outside your lodgings, climb the stairs rapidly three or four times, and have in your room a big heavy stick like a sword and wield it now with one hand, now with the other, as if in a scrimmage, until you are almost winded.

...Jumping is a similar exercise. Singing, too, exercises the chest.

Since the exemplary letter is supposedly from a physician to his medical student sons, we also get to hear the medieval "why" of exercise!

This is splendid exercises to warm one up and expel noxious vapors through the pores, and consume other superfluities...

...And if you do this, you will have healthy limbs, a sound intellect and memory, and you will avoid rheum. The same way with playing ball. All these were invented not for sport but for exercise.

(trans. Lynn Thorndike)

In places where it got cold enough in the winter, people people loved ice skating. Liudwina of Schiedam, a 14th/15th century holy woman from the Low Countries, reportedly kick-started her sainthood career by failing to recover from a skating accident (...because Middle Ages).

But the best example of medieval people actually playing sports takes us right back to uni--Paris this time--where the magistrates got really angry with a group of students for playing tennis in the lecture hall.

You might be interested in this answer of mine from a few months ago.

tl;dr - Yes, people of every class exercised often, usually in the form of semi-competitive play. Wrestling and fencing were hugely popular, and recommendations for abstracted exercise - exercise for the sake of fitness for more complex activities - advocated running, swimming, leaping, throwing stones and javelins, and climbing, among other things.

I’m going to answer from the perspective of medieval Gaels in Ireland and Scotland, since that’s the only part of Europe I’m at all qualified to talk about.

The short answer is yes, people did play sports and undergo training regimes. In the medieval Gaelic world, warriors had the highest social status. As a result, there is a considerable body of literature about the exciting adventures of warrior-heroes (written down c. the 12th century, but drawing from an older oral tradition.) Tales are not documentary – when the hero Cú Chulainn wields eight swords at once, we can’t read that as a literal fighting style – but we can sift through them for glimpses of the reality that grounds the fantasy.

In the epic tale called the Táin Bó Cúlaigne there is a section of the boyhood deeds of Cú Chulainn. He goes to the king’s court to begin his training as a young boy, carrying his toy javelin, a shield, a stick and a ball. He plays along the way by throwing his javelin and running to catch it before it hits the ground.) He meets the boy-troop (made up of all the boys in fosterage at the court. Fosterage was an important custom that involved sending children to be raise partially by someone else, in a situation where they could learn new skills and make valuable social connections. Fosterage of both boys and girls was practiced through all social classes.) Cú Chulainn doesn’t ask the boy-troop for their protection (which would have been the polite custom) and so all 150 of them attack him with their javelins, their balls and their hurling-sticks. Being a legendary hero, Cú Chulainn of course deflects every javelin with his shield, catches every ball and dodges every stick. Then he goes into a rage and knocks all of them down.

So from this we can see that javelin play and some sort of hitting-a-ball-with-a-stick game were part of medieval Gaelic life. We don’t have descriptions detailed enough to pinpoint the way this game was played, but scholars have suggested that the modern sports of hurling, shinty and golf may all be derived from it.

There are also a large number of feats mentioned in Gaelic texts. These are things like running on chariot beams (attested in Julius Ceasar’s account of Celtic warriors in Gaul as well.) In the Táin Bó Cúlaigne the chariot fighters perform these feats on ropes stretched between the doors of the king’s hall – suggesting a tightrope or slackline style activity. Dexterity, strength and agility were on display with feats that may well have included juggling apples, juggling swords, tossing and catching shields, twirling and throwing javelins, various kinds of jumps, jumping and ducking swung weapons, throwing wheels into the air to see who could toss the highest, cutting off an opponent’s clothing or hair without other injury, bringing down live birds with a thrown sword, leaping onto the points of spears and slinging stones. There are a number of feats that we have terms for – the hero’s cry, the breath feat, the eight man feat – without any description that would give clues as to what is indicated. Cú Chulainn is said to practice his feats every morning. There are also descriptions of warriors performing feats on heated stones or in baskets placed in trees. The warriors are usually men, but some of the best are women – in the tales, at least.

The wisdom-text called the Triads lists “performing feats together” as one of the three situations likely to cause strife. Competition and games were part of boasting and gaining status for the warrior elite, as well as part of training for battle. As for people involved in agriculture, exercise was part of much of their daily work: herding cattle and sheep, churning butter, grinding grain on stone hand querns, spinning and weaving cloth, plowing, planting, harvesting, gathering fuel (wood or peat), building and repairing fences, buildings and equipment, washing laundry, fulling cloth by hand, walking as the main mode of transportation, hunting and fishing, rowing boats... Lots of labour-intensive work.

Sources:

Sayers, William. “Martial Feats in the Old Irish Ulster Cycle.” The Canadian Journal of Irish Studies, vol. 9, no. 1, 1983, pp. 45–80. JSTOR, www.jstor.org/stable/25512561.

O'Sullivan, Aidan, and Tríona Nicholl. “Early Medieval Settlement Enclosures in Ireland: Dwellings, Daily Life and Social Identity.” Proceedings of the Royal Irish Academy. Section C: Archaeology, Celtic Studies, History, Linguistics, Literature, vol. 111C, 2011, pp. 59–90. JSTOR, www.jstor.org/stable/41472815.

Táin Bó Cúlaigne, translation of 1st rescension on celt.ucc.ie

Adding to u/sunagainstgold's excellent response, the essayist Montaigne (1533-1592) wrote about physical exercise quite a bit:

"If the mind be not better disposed, if the judgment be no better settled, I had much rather my [young] scholar had spent his time at tennis, for, at least, his body would by that means be in better exercise and breath." (Of Pedantry)

Here he is describing his father in On Drunkenness:

"For a man of little stature, very strong, well proportioned, and well knit; of a pleasing countenance inclining to brown, and very adroit in all noble exercises. I have yet in the house to be seen canes poured full of lead, with which they say he exercised his arms for throwing the bar or the stone, or in fencing; and shoes with leaden soles to make him lighter for running or leaping. Of his vaulting he has left little miracles behind him: I have seen him when past three score laugh at our exercises, and throw himself in his furred gown into the saddle, make the tour of a table upon his thumbs and scarce ever mount the stairs into his chamber without taking three or four steps at a time. "

This description of fitness follows several lines on the elder man's honesty, sobriety, and courtesy. Later, in On the Education of Children, Montaigne writes:

*"*Our very exercises and recreations, running, wrestling, music, dancing, hunting, riding, and fencing, will prove to be a good part of our study. I would have his outward fashion and mien [i.e., shape] and the disposition of his limbs, formed at the same time with his mind. ‘Tis not a soul, ‘tis not a body that we are training up, but a man, and we ought not to divide him."

We see in the same essay that, unlike the classical Athenians or modern gym goers, physical exercise is a question of moral but not necessarily (or entirely) aesthetics for Montaigne:

"Wean [the hypothetical young student] from all effeminacy and delicacy in clothes and lodging, eating and drinking; accustom him to everything, that he may not be a Sir Paris, a carpet-knight, but a sinewy, hardy, and vigorous young man."

Interestingly, but not necessarily relevant to your question, this is the same logic that inspired Freidrich Ludwig Jahn's gymnastic movement in the early 19th century: frisch, frey, fröhlich, frumb / sind der Studenten Reichthumb! A generation of tough, fit men would never fall prey to a foreign (French) army again. I believe you can draw a more or less direct lineage from Jahn's rings and pommel horses to the physical culture of the late 19th century, Eugene Sandow, and the birth of bodybuilding, which continues to dominate the modern conception of fitness.

The most popular game that the Native Americans were playing upon European contact was something called Chunkey, which was translated to "running hard labor". The men of the village would sometimes play all day long.

https://en.m.wikipedia.org/wiki/Chunkey