That would have been even more work, because there was at the time no infrastructure in Setup for having 32-bit-only components. (And then automatically uninstalling it when WOW64 was disabled.) And besides, all the people who criticized Windows 95 as "not really a 32-bit operating system because it has some parts in 16-bit" would use the same logic to say that 64-bit Windows is "not really a 64-bit operating system."
The "besides" point is what I was expecting: there was some kind of rule not to ship 32-bit-only components to claim "full 64-bit support". A rule that was mindlessly applied even to a little game that has nothing to do with the core OS. As I said, politics.
(Not that I personally care, but I've observed that people love those builtin games.)