They're around 8-9cm on average, with about 2cm standard deviation. The tend to force a fairly constricted grip when held with a "hammer grip", whereas when held in a handshake grip with the lower fingers over the pommel (for viking swords), they allow for a greater range of motion and for throwing cast blows.

A similar parallel can be seen in later indian tulwars and Afghan pulwars, which feature short grips and constricting guard and pommel designs.

Tulwars feature a narrow cross guard, a short grip, and a disk pommel, and effectively force a hammer grip. This assists in producing drawing cuts.

Pulwars, conversely, have a dome shaped pommel which allows for a greater range of motion. This is more analogous to the globular integrated pseudopommels of gladius and early spatha designs. Gladius have rounded guards and globular pommels, so they actually have a relatively good range of motion

It's worth noting that you can't do a vast blow with a tulwar, but can with a migration era or viking sword.

It's also worth noting that some historical swords had shortened grips from repair and rehilting, so it's entirely possible that a small portion of extremely short gripped antiques fall into this category.

Precise measurements of viking era swords can be found in "swords of the viking Age" by Ian Pierce, and also in seminal texts like "de norsk vikingesverd" by Jan Petersen.

Measurements from pulwar and tulwars taken from my own collection of antiques for comparative purposes

The grip of the Roman sword in your pictures is quite clearly molded to accommodate 3 fingers instead of the 4 you might be expecting. That certainly accounts for a lot of the perceived shortness. (Although the hilt is broken, so some of it may be missing.)

It should be pointed out that you didn't always wrap all 4 fingers and thumb around the grip. Depending on the weapon and its method of handling, forefingers and thumb might extend along the grip or guard, and little finger might cup the pommel, rather than curling around the grip. Grips were often designed for 3 or even 2 fingers and not a full hand as you might think.

On the Viking swords you are only looking at the tangs. The grips themselves are long-gone. This exaggerates the impression that a whole hand had to fit entirely inside that space, when actually the grip would have filled much of it up. Early Viking grips were often waisted like a spindle, which would make the grip nearly the width of the pommel and guard at the extremities, and narrow in the middle (see the Kragehul Mose swords for examples of surviving grips). That actually makes the narrow part of grip even smaller than the surviving tang suggests, but it also means the hand did not have to squeeze into that small space.

Modern replica swords almost always build their grips too large, because most of the people buying them have no idea how they were actually held or used. (Also, a little bit because we're generally bigger and more well fed than they were, but mostly because we're holding the weapons wrong.) There is also a modern-day fashion for large 2-handed weapons which tends to exaggerate our sense of appropriate sword grip sizes. (Even Star Wars does 2-handed swords, and they're made of light.)

So a stroll through a museum armoury can be a bit surprising, and it's not limited to Roman and Viking era weapons, either. Renaissance rapiers and small swords have grips that seem impossibly small, until you realize the pommel goes in your palm, not hanging out the bottom of your hand. George Silver points out the different grips styles in Paradoxes of Defence:

Yet the Italian teachers will say, that an Englishman cannot thrust straight with a sword, because the hilt will not suffer him to put the forefinger upon the blade, nor to hold the pommel in the hand, whereby we are of necessity to hold fast the handle in the hand.

So the English broadsword of his time was evidently held in a full-hand grip, whereas the Italian rapier put the forefinger on the blade, while the pommel rested in the palm. The rapier grip, in other words, only had to accommodate the middle 2 fingers at most.