TLDR
TBH the wallet is probably more sentimental since he'll get to carry it around all the time and use it. That being said the game is a good idea but it'll be somewhat short term in that once he's over it, he'll be over it. Admittedly you two play games together but even when significant others have bought me videogames in the past, once I finish or get bored of it, it's not like I go looking for it.
Baking (despite being short term too) works well especially if you aren't a good baker and put in a lot of effort to make something.