"It is you choosing your life."

Hans51Is it a short version of 'It is you that choose your life."?

That's what it looks like to me. But I wouldn't write "It is you that choose your life" - that's incorrect. The following three examples are better from the standpoint of grammar and style:

It is you who chooses your (own) life.
You are the one who chooses your (own) lif

XerxesIt is you who chooses your (own) life.

Thank you so much and you still agree that it is a it that cleft sentence, right? And could yo tell me why chooses, not choose there?

Hans51"It is you choosing your life." Is it a short version of 'It is you that choose your life."?

More or less. I see it as "It is you who are choosing your life". Because 'you' is a person, 'who' works better than 'that' in forming the cleft sentence.

Hans51Is it possible to omit that in It that cleft sentence?

Your exam

Hans51you still agree that it is a it that cleft sentence, right?

It looks like a cleft sentence to me.

Hans51And could yo tell me why chooses, not choose there?

For me, who (he/she) chooses. But CalifJim's response above is equally valid. The key thing here, in my opinion, is that when dealing with humans, it is best

Xerxeswhen dealing with humans, it is best to use "who" and not "that".

That appears to be more true of AmE than of BrE.