There isn't a single thing about that uniform that looks remotely like the TOS Klingon uniform.
Not sure why that's a problem, given that not only would it make sense that cultures have varying styles of clothing like they do in real life (within the US today, you got Amish communities which dress in a very conservative fashion drawn from the past, to people who favor low-cut crop tops and short shorts), but DSC is set awhile before TOS when the TOS uniforms were first seen.