1. Balrog chases pussy dwarves out of Khazad-Dum.
2. Goblins move in because no one is occupying the space anymore.
3. 7,000 years pass.
4. Dwarves, none of whom can even remember someone who actually lived there at any point (one would be hard pressed to find an elf that could remember that either), decide they want it back.
5. Goblins are now being killed when it's really now their own land.

It takes 20 years for a squatter in the US to establish homestead rights. Goblins held Moria for 7,000. It's their land at this point. Dwarves are an invading force, goblins are the rightful defenders.

The owner of the land is whoever can hold it using force. There is no land claimed by anyone that doesn't either have the army to fend off all neighbors, or a big brother behind them waiting to back them up.

Time is irrelevant. Claiming to be the first in an area is irrelevant. If you can fend off say... 8 or more countries with enough force to render their army null and void in 5 maybe 6 days, then that land is yours until its taken by someone with more force than you.

Nothing is rightfully anyone's property unless you can defend it.