Is there a way to gift a monetary amount and not a specific game? I would sooner give $ and let the recipient choose what games they like.

I'm afraid GOG doesn't offer something like that yet. I like GamersGate's Blue Coins though and am hoping GOG would adopt something similar... but as of now the recipient will need to make a choice before you buy anything ;)

Gifts from the site are made by purchasing the game and gifting the game code. Your best option for what you want to do would perhaps be to purchase a prepaid visa to gift so the recipient can make their own purchases with that.

Yeah I thought of that. The recipient would probably use those funds for something other than games and I want to specifically force this person to buy games. BUY GAMES, not an electric toothbrush!

Hey those are awesome! But you need to show me where you get electro toothbrushes for $9.99 O_O

Oh well, there is GamersGate's and their Blue Coins like pops117 mentioned. Perhaps gift the person one game from here you think they might really enjoy, and purchase some Blue Coins for them to buy one game from there that can be their own selection.