I know that SBR's are illegal here in the state of NJ and legal with a tax stamp in other states like PA. I was in my local LGS in NJ and he had a Troy A4 with a 10.5” barrel and he told me it's perfectly legal in NJ so, my question is what makes it legal and not considered an SBR. I know it's categorized as an “other”, what makes it an “other” and what prevents me from building an “other” because he made it sound not too simple to do? Is it just as simple as putting a SBA3 brace on it? Thanks in advance.

The simple answer is it's not a rifle because it's not designed to shouldered and it's not a pistol because you are supposed to fire it will both hands (fore grip).  Same as the designation of the Mossberg Shockwave and Remington TAC-14

Its a firearm because:

It’s not a rifle because there is no stock thus, not meant to be shouldered
It’s not a pistol because it’s designed to be fired with 2 hands, hence the VFG
It’s not an AOW because it’s over 26” in length (end of buffer tube to barrel tip)

If you want to build one from a stripped receiver, go ahead. Plenty of people have. Just understand the rules because you don’t want to build an AR pistol (not legal in NJ) or an SBR (felony without a stamp, and also illegal in NJ).

If you want to build a shorter version, AOW are legal in NJ but you gotta follow all the steps regarding NFA items before you put it together.