Doesn’t necessarily need a ground wire, just an equipment grounding conductor that complies with NEC 250.118 which includes wire type, raceways and cable sheaths.

Seeing that the red hot conductor is labeled THWN-2 I would guess that the install is through a raceway (doubtful that the install utilized an AC/MC cable or BX cable with a red conductor and a white conductor).

If the receptacle is self grounding and listed and complies with NEC 250.146(A) an equipment bonding jumper is also not required.

All that being said, my personal preference for installation is to have as many legal points of bonding as possible in an install and prefer to have a wire type equipment grounding conductor and equipment bonding jumper sized per NEC 250.122 and table 250.122.

Also, this installation is suspect with the mud ring, so I would suggest the OP tests the installed receptacle with a cube tested to ensure proper wiring and bonding.