I'm not familiar with this one, either.
Gams is slang for legs, so unless it's some reference to walking with or hanging out with (throw a gam(leg)=walk?)
Unless it's a typo for throwing the game - which means to purposely loose a competition in order to receive some kind of payout for rigging the match. That doesn't quite seem to fit into the context here either.
Some of these sentences you've been posting sound like the writer was mixing old west slang with hardboiled noir lingo. Red sounds like some kind of 30's gangster transported back in time 75 years to the Wild West.
Not sure if that's the actual plot, or just flaky writing....
Interested in Language