Excellent! And the screen readout indicates that he's a full lieutenant rather than a j.g.
The lieutenant junior grade rank evidently wasn't used in the 23rd century. There was just one step in rank from ensign to lieutenant.
Joe Tormolen in TOS was a Lieutenant JG. ("The Naked Time")
And even if the j.g. rank was only rarely used in the 23rd Century of the Prime Universe, it's possible that this may have changed in the Kelvin Universe.
(Yes, I may well be fudging things there, too--but I'll take anything that makes Kirk's promotion at the end of ST09 look less implausible, even if we're only moving from a four-grade to a three-grade promotion.)