Trying to run this through Steam so I can use the overlay to view a guide while playing (alt-tabbing puts the game in windowed mode so I can't do it that way). However, the only shortcut I can get to work in Steam is the DOSbox one in the GOG=>AITD folder and that just opens DOSbox, not the game itself. The shortcut that I have on my desktop that opens the actual game has a funny path that Steam doesn't like/understand. Has anyone figured out a trick to getting this working in the Steam client?

My thoughts are it is because the game is not Steam native, and thus its features are not integrated.
I doubt the reason is DOSBox, I guess if you use Steam to launch, let's say, Starcraft or WoW, Shift+Tab won't work too (well, it is so for Planescape: Torment, this I can say).

And yeah, the option page with this feature in Steam says it is built in games... =))

I've noticed that if i disable hardware acceleration in Plants vs Zombies, the overlay doesn't work, it only works with acceleration on.
Perhaps its something similar, and you need to use OpenGL in the graphics settings of GoG to get the overlay to work.

I don't know why the overlay doesn't works with all non-steam games, but it doesn't work with some steam games too.
For example: I have tomb raider legend, anniversary and underworld on steam, the overlay only works on tomb raider anniversary.
As for non-steam games, it's the same, depends on the game. Mafia 1 I played using the steam overlay before the game came out on steam, so it has nothing to do with the game being on steam. With Diablo II and Starcraft the overlay doesn't work, but with Starcraft II it does.

The Steam Overlay requires a DirectX 9 compatible title.