Newcomb's problem applies just as much in real life.

Not unless you believe in gods. Omega is just a locally popular name for "a god".

I could in real life appraoch you claiming to be Omega, or as an agent of the Matrix or whatever. How would you respond?

Depends on the circumstances, but the set of possible responses includes "nod and slowly back away", "laugh", "make a note in the contacts list saying 'batshit crazy'", "look for someone to take care of you until the drugs wear off", etc.