The impression I get is that he watched TOS as a kid when he was too young to understand many of its nuances but he's watched the TOS movies more recently and enjoyed them because of the increased action quotient (and in fairness I think this is important in a movie as opposed to a series). The absence of Chapel and Rand but inclusion of Chekov lends some support to this.
His comprehension of how Starfleet should be organised or what its ideals were meant to represent seem to be very ropey. He seems to have only the most basic grasp of what level of tech existed in TOS or the butterfly effect of changing those parameters. He doesn't seem to understand the way Trek was based on naval tradition or why that mattered.
He seems happy to keep the women in their place though.
Star Trek as a franchise has had numerous series and movies to establish what Trek is. JJ has only had 2 movies to do that.