I can think of a few places that meet the description, but it doesn't really matter where it was.
It's not unusual to mark a much smaller runway on a large old runway. The reasons are straightforward enough - the full bigger runway isn't needed, and would cost a fortune to maintain, so they mark as much as they actually need, and maintain that bit properly. The rest is manoeuvring area. Taxiways might be marked, but usually they're not.
So, if you're on the marked runway, it's a runway. If you're not (but on the big old runway) take care as there are probably potholes, but the etiquette is basicallly the same as if it was all a big grass field with a runway marked - taxi as per commonsense and local instructions, stay off the marked runway until it's appropriate to enter it. Do your run-ups where you aren't in anybody's way (or where told to, if there are local instructions about it).
If you were well off to the side of the marked runway, then the aeroplane landing was incorrect. On the other hand, he could have had any number of reasons for needing a bit of elbow room, so your amiably moving further out of the way, so long as it didn't take you anywhere unsafe for your aeroplane, was aeronautical good sense and manners in my opinion.
G