Yeah - it looks a bit 'WIP render' in that video. Although I'm a little curious - apparently they have gone with a design inspired by the unused 'Planet of the Titans' concepts by Ralph McQuarrie (after Ken Adams), so the finished Discovery might well wind up looking something like that version, at least:
(note the wider, flatter secondary hull, and the nacelles which are rear-mounted/forward-projecting, more like the TNG Enterprise-D than Kirk's Enterprises - hmm...)
That's the other thing - I'm wondering when this is going to take place era-wise. Obviously we're back in the proper Trek universe (hurrah!!), but the rumours suggested the new series was going to take place in the time between The Undiscovered Country and TNG (which is a long stretch of time to play with, with a lot of stylistic changes during those years).
Obviously the registry is NCC-1031, which is earlier than Kirk's Enterprise (NCC-1701), although to be fair, registries from the TOS/TMP era are a bit of a muddle - you've got the Constitution-class USS Constellation (NCC-1071 - and yet supposedly a contemporary ship to the Enterprise) in The Doomsday Machine, and in The Search for Spock, the Oberth-class USS Grissom (NCC-638), which can't be older than the Constitution-class, since it has design elements more in keeping with ships from that time, like the refit Enterprise and the Excelsior (the glowing blue deflector dish, for one).
(heck, that 'ribbed' ring around the bridge section on the Discovery's saucer isn't a million miles away from the similar design on the Grissom, come to think of it...)
Throw in the fact that a lot of the designs from the TMP movie era played around with more experimental geometric designs, harder angles, and unusual configurations than the more curved designs of either TOS or TNG-onwards, and that not only was 'Planet of the Titans' an abortive attempt at a post-TOS movie series like TMP, but the mock-up study models even showed up as background ships in Earth Spacedock in The Search for Spock and The Voyage Home, and ...yeah, it's not beyond the realms of possibility that the Discovery is just going to be a more extreme design from the TMP era.
...or it could be a bit of overly-referential fan-w**kery, re-using the McQuarrie design instead of coming up with an original design more typical of the era.
And that's even assuming
it's indeed of that era - could well be the whole thing is a glaring anachronism. We'll see...