Mortimer McMire is the grandson of Adolf HitlerSince Keen is the grandson of B.J. Blazkowicz, who fought Hitler in Wolfenstein 3D, so who knows how far the rivalry goes back? It would also explain some of his beliefs.
Mortimer McMire is the grandson of either Dr. Schabbs, or Otto Giftmacher.Perhaps Mortimer inherited his views from Naziism, but his genius from a scientist instead of Hitler himself. On the one hand, Schabbs seems to be more of the supergenius that would create a mastermind like Mortimer. On the other hand, the McMire name may be a bastardisation/mutation of Giftmacher, which literally translates to "Poison Maker".
Molly is dating Billy's older brotherThe games mention him having a brother after all. I know there's nothing to support this WMG, but it sure would make Billy and Mortimer's rivalry more interesting if their siblings had the hots for each other (and by interesting, I mean more vomit-inducing for both boys).
Keen is a murderous psychopath who really, really hates the VorticonsIn the first two games, all the Vorticons Keen encounters are soldiers trying to blow up the Earth, and thus fair game. Then you discover in game two that the Vorticon's aren't really evil, they're just under mind control by the Grand Intellect aka Mortimer McMire. Unfortunately, you still have to shoot your way through the mothership. Sacrifices have to be made to save the Earth, after all. But then game three rolls around and Keen goes to the Vorticon homeworld to face the Grand Intellect once and for all...but not before rampaging across the entire planet and wantonly slaughtering its inhabitants, including breaking into their houses and schools, killing everything inside (including women and children,) and then eating all their food. Hell, they probably only gave Keen a medal at the end of the game in an attempt to keep him from continuing his killing spree.
Keen was traumatized by his actions on the Vorticon Homeworld, which led to the development of the Stunner pistol.In a sharp contrast to above, Keen truly regretted the Vorticon genocide he was forced to perform in order to stop Mortimer. Realizing the horror of what he did, slaughtering even Vorticon children, out of necessity, Keen developed the stunner pistol he now uses so that he never has to kill an innocent again. It's designed to be recharged by any standard pistol ammunition, so he can keep it charged no matter where in the galaxy he battles evil.
Keen grew up in Nazi dominated AmericaBilly Blaze or Commander Keen is descended from B.J. Blazkowicz. The Nazis won the second world war in The New Order and subjugated the world. Billy's absurdly powerful rocket is built from tech that was reverse-engineed from Da'at Yichud artifacts.