The issue with answering this is the nature of the question. What's the limit where you start considering it "inflation"? Is it just something you have to feel? Is it in relation to other games in the same period?

You are correct to assume that it's pinball. The reason for this - even though other types of games had scores - was because pinball specifically encouraged high scores. The earliest pinballs had specific "skill shots" where you could make your score higher with exacting proficiency. It was difficult to hit the upper limit, whereas with countertop gun games there was a way to get a perfect score.

Of course there were often incentives to getting a high score, but it was not universal that pinball and other coin-op games were used for gambling. It's clear enough by looking at many of the 1930s tables that there are those tables with direct incentive for luck and direct incentive for skill. Most notably, the table Advance (1934) - designed by Harry Williams - has a progressive scoring structure. In order to get to the highest scoring holes, you have to land a ball in a specific hole then get another ball to that same area so it can travel over the once open hole. This presented the first time that you could easily outdo a single average play of pinball with one score. Is that score inflation?

Once we get beyond "gobble holes" being the only feature of a pinball table, it becomes theoretically possible that you could score an unlimited number of points. However one issue you find with the introduction of bumpers in Bolo (1936) is that there is no score totalizer. Keeping track of score wouldn't become very common until after WWII, and getting such high scores wouldn't be quite possible until flippers came into the game. Humpty Dumpty (1947) still had gobble holes, but you could hit bumpers repeatedly. The score tracked in terms of increments of 10,000 with an upper limit of 790,000. This wasn't unheard of at all, games the same year had similar scoring boundaries even though it was harder to get points.

Maybe a million points is required? How about a billion? A special promotional pinball table promoting the film The Time Of Your Life (1948) was extra size with extra points. It was made in very limited quantities, but as a spectacle I think it definitely qualifies as score inflation. Maybe it doesn't count because it wasn't widely available. Million point scores started showing up in 1948/1949, Gottlieb's table Bowling Champ (1949) as one example. Maryland (1949) by Williams took it to a maximum of 9,990,000. Again, is this what we're looking for? The scores for each individual action have gone up in this time period but what's the point at which we've reached "inflation"?

It should be clear to see why it's nice to get a big score. If a score indicates accomplishment, then adding those zeroes makes it feel even grander. However, there is an upper limit to these things where merely growing the amount won't continue to provide that seratonin boost (unless it's part of the theme). Plus, in the case that you mention above, it's easier to create delineations for different sorts of tasks. Remember the South Park episode where they only got 2 exp for ever boar killed in WoW? If they were just tacking on the zero, that would by 5 times less punishing.

Answering the question of how exactly score inflation begets experience inflation is a far more specific question it would take a lot of time to answer. I can't specifically say whether this first occurred in tabletop games or video games, but early video game RPGs tended to keep to one or two digit experience gains in early encounters, climbing along with difficulty to create a more advanced curve that couldn't be circumvented by fighting low level monsters endlessly. Again this is a big topic and I think in terms of answering the question of origins for "score inflation" that I've provided a good base for narrowing what you mean by that question.

Sources:

Internet Pinball Database - A general collection of information on pinball. Wonderful resources with photos from which to learn more about the game.

Encyclopedia of Pinball (Vol 1 and Vol 2) by Dick Beuschel - The great, late Dick Beuschel's most important works on pinball. No longer in print, but absolute gold for determining the origins of the game and early innovations.