Q:

Why wasn't Loki imprisoned on Sakaar like all the other slaves? 

In Thor: Ragnarok, why is Thor captured and forced to be a gladiator, but Loki can just walk around and be friends with the Grandmaster?  

A:

So Loki falls out of the Bifrost, and lands on Sakaar. 
The scavengers come for him; Loki does his projection, "I'm not there, I'm really here, honestly," trick; they don't capture him.  
He uses his magic to say hidden & observes what's going on, then cozies himself up to the Grandmaster, telling him something he wants to hear (because it's easier to stab someone in the back when you're close to them and you've gained their trust). 
I don't know if this is what actually happened, but it's Loki's modus operandi and it's how I see it going down.