Well, For some reason, He finds Gordon special. I mean, He set him up (Sorta) at Black Mesa and gave them the crystal to use, Which he knew would put Gordon in the hands of escaping Black Mesa, And Saving the world.
He has a "Job" That he needs to do, that's he uses Gordon to do. Gordon could be said as "Gman's Puppet" Gman can control what he does by putting him in a different dimension I guess.
Pretty much, I think Gman has been assigned a Job by someone (Possibly his boss? He does have a suit and a suitcase. Making me think he works for someone) G Man thought, Hey Maybe I can get a Physicist to go and save the world for me...Again (Gordon saves it twice, If you didn't know :P)
Im kinda confused about GMan, What he does, and what he's for. I just thought of all that at the top of my head, so it might be a bit confusing. I think it makes much more sense then Gman being related to Gordan freeMAN. That theory is old...