I'm not clear as to why this is a debate question. The very definition of "domestic" takes into account those born within the borders of the United States. As with domestic food and drink - there is a clear distinction as to what is foreign and what isn't. Omar Mateen's New York state birth absolutely makes his actions one of Domestic Terrorism.
Yes, being born in Queens makes Omar Mateen's horrific act of violence an act of Domestic Terrorism. There is no evidence that he is in any way connected to ISIS. Furthermore, the act seems to be directed against gay people not Americans in general. There is no reason to believe in a terrorist connection.
Terrorism is any act of violence committed to incite or induce terror in a population and definitition of domestic can mean home, or home related. If he was born on US soil, and committed this act of terrorism, then yes, he is a domestic terrorist. There is no other way to look at it. It doesn't matter what his association was, or what his purpose was... the base purpose was to induce terror, and that he did without question.
Threats to American safety don't just come from abroad: sometimes they are homegrown in our own backyard. Omar Mateen, the perpetrator of the Orlando nightclub attack, was born in Queens and was a naturalized American citizen. This makes him a domestic terrorist who was compelled to commit acts of violence against his fellow Americans.