This isn't new in Trek though. No one was going to describe the TNG/movie Klingons as Klingons without context coming in with only TOS background. Discovery's just doing what the franchise did before.
There's a bit of a difference for TMP, though. The first thing we see are the Klingon ships, and they look exactly like the ships from TOS, only much better detailed. That's pretty much a dead giveaway that the aliens we then see next are Klingons, despite the bony ridge going across the tops of their heads, and their uniforms, and without any swarthy makeup, and the fact that they are speaking in their own language (which are the only things differentiating them from the TOS Klingons.)