Definitely not the City of David. I don’t understand why people jump to such conclusions. Maybe it’s a desire to puff up the importance of their work.
One possibility for the location shown on that map is that it’s Gibeah of Kirjath-jearim. When the Philistines returned the ark of the covenant in Samuel’s time, it was kept at Kirjath-jearim until David brought the ark to Jerusalem. The location you show on the map would be a logical stopping point for the ark coming back from the Philistines.