Multiwina? I'm LOVIN it atm

Operation: Flashpoint (get it on Amazon) or ArmaA 2 would fit the bill for thinking shooter.

I'll second that recommendation. Your dad seems to love tough games were every move has a potential consequence. Commandos is tough as nails but very satisfying when you beat a level.

I agree...

Or even Civilization Revolution. That game is truly a thinking man's game.

I'd say Evil Genius or something from the Commando series.

Roman5 nailed it and in order too. The Commandos games have abnormally good reviews on GOG (i.e. they don't just gush), read them to convince yourself.

I'd only add Serious Sam to the list, but Painkiller is better for most folks.

Try Panzer General II

Shooters ... chess ... why not giving him something new to try? Like an offroad racer (1NSANE) or a Pinball (Pro Pinball)?

Has your dad ever played with a Civilization game? As far as turn-based strategies go, they are probably the best.
GOG recommendations
For shooters, Painkiller is indeed a very good choice.
As for turn-based strategy suggestions, Panzer General 2 is a very good (and popular) game, or, if your dad can enjoy a sci-fi setting, do him a favor by grabbing the Master of Orion pack. I've not played MoO1, but the second instalment is incredibly good.
Alternatively, you could get for him the Lords of the Realm pack; according to my experiences, LotR2 is one of the best medieval TBS games.
For a real-time and very demanding "thinking game", check out Soldiers: Heroes of World War 2.

A call-girl ?

Thanks for all the suggestions! I've got a few ideas now, and I'll tag the solution button when I've decided and there's a little more time between heading over to the relatives'. Merry Wintermas, and so on.

Oh, I forgot to mention Conquest of the New World yesterday. It's a very well-made, comlpex TBS set in the colonization era where there're many strategical and a number of tactical decisions to make.
Happy holidays to you, too!

I wouldnt mind that as a christmas prezzie, dunno what the other half would make of it.