Garcia and Final Atomic Buster (and Sirlin and I, a little bit) have discussed this matchup a lot.
It feels really bad for Rook, but is probably more even than it feels.
Sirlin says he very very rarely loses to Geiger as any character, and Garcia says he beats nearly everyone he fights when playing Geiger.
So I really want challenge matches to happen, so we can see who is right!
As for my personal take on the matchup, Geiger is definitely at an advantage. Spirals, Gears and air kicks all keep Rook out very well. So I realised that Rook's ideal range is not actually what you might think.
If Rook is standing about two body lengths away from Geiger, that's a bad range. Because Geiger can throw Spirals that Rook can't do anything about. If Rook tries to jump forward, Geiger can Flash Gear. If Rook tries to jump neutral (or forward) Geiger can j.A, which beats all of Rook's air options.
The ideal range for Rook is slightly closer to half screen; the distance that Rock Armour travels. Because from that range, Geiger can't punish Rook for jumping (without jumping forwards, but that means Geiger is coming to Rook??), and if Rook gets a knockdown with Thwomp, he can Rock Armour right over to Geiger's poor, knocked down body. Then he starts up the blender.
Good luck, and happy Gear hunting!