Record player sounds out of tune and "wavy"

I've been trying to diagnose this issue for a while. My records all sound slightly out of tune and "wobbly". I've tried old and brand new records and they all have the same issue. It's not an obvious thing to hear, but I can definitely hear it when I pay attention and it drives me crazy. Is it possible I set up the turntable wrong when I took it out of the box and assembled everything? Something with the belt? Or could it be a needle issue? I'm pretty much a turntable newbie, so I'm hoping there's some glaring error I'm unaware of. 

I don't hear the problem when playing anything else through the speakers (Bluetooth, Spotify, movies, etc.). I've also tried placing the turntable on the ground or making sure the table's surface is completely level. Still has the same issue. 

Here is a short clip to give you a sense of what I'm hearing. I hope you can hear it too! Any help is much appreciated! By the way it's a Kenwood KD-291R.

CLIP: