Relinquize/lose ground

Yes.

Means 'go back'?

Be forced to go back, yes.

pushed back?

What about drived/drawn back?thrusted back?shove back?elbowed back?shouldered back?forced back?knocked back?impelled back?propelled back?compelled back?hustled back?nudged back?

Stick with 'relinquish ground': that is formal and what was intended.

But the other paraphrasings I offered also mean the same thing, right?

They all have their nuances, some appropriate and some inappropriate, which I don't really want to run through. I don't have time to annotate your thesaurus.

Yes it means he is forced to give up land, pushed back, lose ground. Relinquish is to let go of something.