So, in order to keep people from being confused that the new series is part of the JJ universe, they decided to create a third universe. Yeah, that makes sense.
In order to keep people from being confused that the new series is part of the JJ universe, they decided to entirely copy the style of the JJ universe rather than stick the the aesthetic of the prime universe they're claiming it's set in. Seems legit. These are very close to JJ Klingons, but barely resemble anything that was ever shown on TV.
People mention that the look of the Klingons changed from TOS to TMP as justification, but to me there's a huge difference between changing the look of aliens from an old TV show that ran for 3 seasons with limited budget and resources, and a TV show changing the look of aliens after 600+ episodes from 4 different series and 10 films over the span of almost 40 years portraying them pretty consistently a particular way.
I would have even been fine with them making them look like the TNG> era despite them appearing very differently in TOS, but you don't just change them because you feel like it when the show is set so close to TOS.
I feel like the people behind this show aren't aware that Star Trek existed before 2009.
That's definitely the feeling I get from the show, at least visually. The new phaser, communicator, and tricorder props are actually very well done, but everything else is unrecognizable.