Frosty Rebellion

I mean... Even Doom had a button to switch between turning and sidestepping, didn't it? (I think it was Shift?)

Trivia: In fact, "strafe-running" is actually used for solving a few Secrets such as the secret exit in E3M6, as Doomguy actually moves a tiny bit faster diagonally than forwards and exploiting this is necessary to "fall in style" far enough to reach :P