How do games choose what version they are in?

The games don't decide it. The developers do when creating the game and adding onto it.

Version 1 and version 2 sound like they would have huge differences between them.

But how about version 1 and version 1.1? Sounds like minor difference, right?

Because that's the case. Smaller updates, such as quick hotfixes or balancing get smaller numbers. Usually, if a game is in 2.35, a hotfix patch would bring it to 2.36. If they released more content, it would be 2.4.

It will continue to climb from 2.35 all the way to 3 over the course of months, maybe years. Game development is slow, timely, and taxing.

For many developers, they take steps before hitting a goal. So lets think of the 1st number as a main version, 2nd number as a goal, and the 3rd as steps. They make a bunch of steps to fix bugs and tweak things, then when they have it all down they can make the goal. Now for the first number, i know minecraft itself was in beta 0.#.# Ex. 0.7.3 and that is the reason for the zero, and after full release it became 1.#.# Ex. 1.7.2 so its their way of saying that the game has hit a whole new concept or version. Usually the 1st number impacts the game much more than the 2nd number, so it could also be by the amount of change the game has been given(going back to what i said earlier). The 3rd number is for small tweaks and bug fixes. 2nd is for a medium sized update with more content, and 1st number is the big thing representing a new milestone in the program. This may be a bit off, but hopefully you get the gist of it. Hope this helps.