I recently bought a 13-inch Macbook Pro (without the retina display) for college. How good will it be for gaming, including my good old games? Here are the hardware specs from Apple's website:

2.5 Ghz dual-core Intel Core i5 processor
4GB of RAM
Two video cards are listed, I can't tell if that means the Mac has both or what. They are: Intel HD 4000 and NVIDIA GeForce GT 650M

Better than my MacBook Air, which is at approximately half those specs. I can run stuff like Left 4 Dead 2 with some hiccups, Killing Floor considerably better, and virtually any Mac game from the Humble Bundles or GOG except the Witcher games.

It has both video cards. The Intel HD4000 is an onboard chip, and it can switch to the 650M when needed (Note: may need some configuration with each game).

So if I'm running something the Intel can't handle, the Mac will say "oh crap, call for backup" and switch to the NVIDIA?

Those are plenty good specs. You should be able to run 99% (if not 100%) of GOG's catalog with it. That is, if you decide to make use of booting into Windows. Results for getting games to run in OS X via Wine(skin) or other means, without GOG having them Macified first, may vary. I'm not entirely sure how OS X handles those situations but it should switch automatically... with emphasis on should.

I haven't ever had a laptop with dual graphics, much less an Apple one, so I can't speak from experience, but, yes, that's how it's supposed to work.

So are those video cards any good? I'm going to assume the Intel is shit, but what about the NVIDIA?

The HD 4000 should be about half-decent (the 3000 and older were pretty much excrement on a chip though), though of course the GT 650M blows it out of the water and should manage pretty much anything you throw at it (the problem isn't the hardware, it's the software, graphics drivers released by both Nvidia and ATI for OS X are quite a bit behind in both performance and OpenGL features compared to those on Windows and Linux). Though, being a mobile chip, it'll likely struggle with the latest games at the highest settings, but lower them a bit and you should be fine.

The apple site is confusing me. One page says both the 13 and 15-inch have the NVIDIA card, another says only the 15-inch has it. I won't be playing any really "modern" games besides Minecraft, so hopefully this is a moot point.

I would have asked these questions before buying the computer.

Your system properties should tell you.
Apple menu->About this Mac->More info...

Judging from this page then the MB Pro on the left-hand side is the one you got: In that case, yes, it only has Intel HD 4000. As said, that chip should do well for most older games and some newer, but definitely not the newest of the new.

Sidenote: It also shows once again how horribly overpriced Apple products are. For an extra $100 I got a 17" Windows lappie - bought at Best Buy for $1,300 rather than the ridiculous RRP of $1,600-some - in March 2.4 i7, 8GB RAM, 1TB HDD, and a GTX 670M /w 3GB. Sure, it might be a beast in size comparison - not all that portable - and it's not quite as shiny, but I'm getting a hell of lot more out of that deal for comparatively less amount of dough.

Looking at the options in the Apple Store, none of the 13 inch versions have the GT 650m, just the Intel HD4000. Which if thats the case, no it won't be good for gaming.

You will be able to run a lot of older stuff fine, but newer games or demanding games like Witcher 2 will have to have the settings lowered quite a bit. Also if you have a retina display Macbook, the HD4000 won't be able to run much at the native resolution.

Not that much will be retina-aware anyway, and thus only get "half" resolutions as options. But that's a moot point, since the OP specifically mentioned that it's one without the retina screen.