How would you interpret this phrase “doing his Mr. Big thing”?
How would you interpret this phrase “doing his Mr. Big thing” mentioned in the last but one sentence?
I would think it means the man, Gelfand, was commanding the other man, as if he was an important man.
What do you think?
Thank you.
PS: the excerpt is taken from “Kneller’s Happy Campers” written by an Israeli author, Etgar Keret. And I’m reading an English translation.

the context:
“C’mon.” Gelfand wouldn’t let it go. He put on his grody leather piece. “Where to?” I asked, trying to stall. “Superdeal,” he announced. “Let’s go get the reward they owe us.” “Us?” I asked. “Just come on and stop jawing,” Gelfand commanded, doing his Mr. Big thing. So I shut up and went.

Question

How would you interpret this phrase “doing his Mr. Big thing”?
How would you interpret this phrase “doing his Mr. Big thing” mentioned in the last but one sentence?
I would think it means the man, Gelfand, was commanding the other man, as if he was an important man.
What do you think?
Thank you.
PS: the excerpt is taken from “Kneller’s Happy Campers” written by an Israeli author, Etgar Keret. And I’m reading an English translation.

the context:
“C’mon.” Gelfand wouldn’t let it go. He put on his grody leather piece. “Where to?” I asked, trying to stall. “Superdeal,” he announced. “Let’s go get the reward they owe us.” “Us?” I asked. “Just come on and stop jawing,” Gelfand commanded, doing his Mr. Big thing. So I shut up and went.

Answer

The words "doing his Mr. Big thing" can be replaced by "pretending/claiming how important he was as he often does".

"Mr Big" phrases like this is often used in a mocking and critical manner. 
If I say "He thinks he's Mr Big" I am saying "he thinks he is important, but it is all in his head. He is the same as the rest of us ... or even less important than us"

'doing his Mr Big thing' is a variation of this.
Adding 'thing' after 'Mr Big' is saying that this behaviour (claiming he was important when he had no such capability) is almost a routine. He's done it before many times, perhaps.

Answer

Yes you are right. - Playing the boss or the most important man.
https://idioms.thefreedictionary.com/Mr+Big

Whether this is an accurate translation is another matter, I can't answer that.