In this example that you gave, INCLUDING UZIS AND PISTOLS is an appositive phrase which must be set off completely by commas. In other words, the sentence must read like this:

"HE GAVE HIM A BUNCH OF GUNS, INCLUDING UZIS AND PISTOLS, AND HIS GODFATHER MOVIE COLLECTION."

INCLUDING UZIS AND PISTOLS is also a subordinate clause which means it is not essential to the meaning of the sentence--therefore, it must be set off with commas. If you remove the clause from the sentence, it still makes sense. You don't lose the meaning nor have you disturbed the subject or verb.

The part of the sentence: HE GAVE HIM A BUNCH OF GUNS is an independent clause, INCLUDING UZIS AND PISTOLS is an appositive phrase, and AND HIS GODFATHER MOVIE COLLECTION is a dependent clause separated by a comma from the independent clause with or without the appositive phrase.

Clauses and phrases are very tricky. I've known many students who have almost pulled their hair out trying to make sense of them!!

~~ Lollie