You know, some programmers build game __engines__...
More seriously, the first programmers were electric/electronic engineers, so the engineer title was probably inherited. And game engines actually require lots of math and physics.
I don’t doubt working on game engines is hard (I do web development). If you build game engines then you are probably a game engine developer. I don’t hold a degree in engineering myself; no shame of not having the “engineer” title.
More seriously, the first programmers were electric/electronic engineers, so the engineer title was probably inherited. And game engines actually require lots of math and physics.