Is an aborted landing considered an incident for the FAA?
It depends.

There are two general situations.  One where the other aircraft was supposed to be on the runway and one where it was not.

In order to increase traffic density and keep the system working, aircraft do not wait for the aircraft landing in front of them to clear the runway or, in single runway fields, for the aircraft taking off in front of them to get airborne.  The separation distances and times are such that normally, the other aircraft will clear the runway but sometimes it doesn't work out.  A departing aircraft might have been given a clearance to take-off but doesn't respond quickly enough, or a landing aircraft might have a problem causing the pilot to stop on the runway to check it out or perhaps simply missing the turn-off they were supposed to take.

ATC might see this happening before the landing aircraft does and issue an instruction to "go around" or, the pilot might have seen that the runway was not clear and made the decision to do so.

This happens around the world dozens of times a day and is not reportable.  The system worked as designed and safety was not compromised.  It is most likely to be what happened in your case.

The other situation is where the other aircraft should not have been on the runway, called a "runway incursion". It might have been instructed to "hold short" of the runway but then entered it or might have mistaken the runway for a taxiway. 

This is reportable. The captain has the authority and the duty to ensure that the runway is, or will be clear when they land and to abort the landing if not.  If the captain cannot be sure, they are required to go around rather than press on in the hope that it will be clear. Again, the system worked but safety margins were compromised and thus, the incident is reportable, both by ATC and the landing captain.  If it was a runway incursion, the crew causing it, assuming that they realise that they made a mistake, are also required to report it.

Although I've mentioned aircraft, there are many things that might not be authorised to be on the runway such as people, ground vehicles, animals, construction equipment etc.  Occasionally, pilots are attempting to land on the wrong runway, perhaps one closed for maintenance, and will go around when they see stuff on it.  These are all reportable.