Games automatically deleted from external drive

Yes, certain games will require being installed on the internal drive - or will require a certain amount of space be reserved over top of their actual installation space. This may be the case with Doom 3, I’m not sure for that specific example unfortunately.
In general though, when you are in the manage games menu and choose to move the location of the game, selecting “Copy” creates a new copy in the location you choose, and leaves the original copy in the initial storage location. Selecting “move” will create
a copy on the new location you choose, and deletes the original on the inital storage place. Or to explain it another way, selecting copy will leave the game in two places, selecting move will leave the game only in the new location you select.

Check a this links:

https://support.xbox.com/en-US/xbox-one/console/manage-storage

https://support.xbox.com/en-US/games/troubleshooting/console-doesnt-detect-external-storage

Why are you copying the game over instead of moving it to the external drive? That way you don't have to delete it after you moved it.

And maybe you accidentally already moved it, and deleted it from the external drive when it was already moved (deleted) from the internal drive.

I do move, but it seems the games just copied, and when i check whats on my drives the games appear on the internal and external drive, then when i delete from the internal drive, the game also deletes from the external drive?

I remember when i dowloaded doom3 it did say must be installed on the internal drive, are some games restricted to only allowed to be on the internal drive?

If you have an external hard drive transfer the game over, then delete it off of the external drive.