The Kelvin was the name of the ship from the beginning of the first Abrams Trek. The one that George Kirk blew up on so we could have angry sorta-delinquent Chris Pine Jim Kirk.
The more I read about continuity and timeline setup, the more I'm convinced that they should've just said this was set like 70-75 years before original Trek. Saying the show is set around the early 2190s/early 2200s would've avoided all this continuity slog. because it could then be considered canonical for either universe.
Pulling dates from the Star Trek Wiki (Memory-Alpha.org).
Green events are canon to both timelines,
blue to the Abrams movies,
red to the original tv shows/movies.
2155: The Coalition of Planets is formed, depicted in the finale of Enterprise
2233: The Narada emerges from a black hole and ends up in battle with the Kelvin, causing the Abrams Trek splinter timeline.
2245: Original 1701 (no bloody A, B, C, or D ) Enterprise is launched under Capt. Robert April.
2250s-60s-ish: Capt. Pike takes command
2258: Events of the first Abrams-verse movie. Kirk is promoted immediately to captain of the Enterprise after the battle with Nero
2260: Events of Into Darkness
2263: Events of Beyond
2265: Capt. Kirk (prime timeline) takes command of the Enterprise
There's like 80 years between Enterprise wrapping and the timeline fracturing because of Nero that they could've used to set this show in where they would've had boatloads of freedom to do whatever they want without consequence. Instead they're alleging that this is "10 years before Kirk and Spock" which, presuming they mean 10 years before the two of them are together on the Enterprise in the events of the original show, puts it somewhere in the neighborhood of 2255. This means that the show is taking place in and around Pike's Enterprise missions (but possibly/presumably before Spock was assigned there) Which feels like it's going to make a mess of things because now you're kind of tangled up in whatever things are happening in the area around TOS' premiere and first run of episodes.
Also I don't think the stylistic choices of the Klingons or whatever have to matter in terms of determining the universe. Not any more than the stylistic differences between TOS and TNG matter (smooth headed "mongolian" Klingons vs ridge-heads, smooth-headed, identical-to-Vulcan romulans vs the "v-ridge" forehead Romulans of TNG) or even the more radical changes from TOS to the first 6 movies. Just because everything looks evocative of the Abrams stuff doesn't mean it has to be Abrams-verse. It's just as likely that they decided to pull from those movies just because they figure that casual non-Trekkie fans would mostly know of the Abrams movies and not all the other works and this would feel more familiar and inviting to them.