That would drive me crazy. Here is an old thread with people asking about the same issue. There are a few solutions in the thread. I would test a small spot before trying a home remedy on the whole floor.

https://www.houzz.com/discussions/2392618/smudges-and-paw-prints-on-ceramic-tile

The vinegar isn't strong enough to clean 'oil' prints like skin oils (foot prints). You need a better 'degreaser'. Your situation is one of the most complained about. Dark, low-gloss flooring showing oil prints.

You can try a spritz of Windex on a tile, let it sit for 30 seconds then wipe it up. Spritz the tile again and then wipe up immediately with a NEW cloth. Walk away for a n hour or so. Then go back and 'reassess' the tile you just cleaned. If you can see the difference then you know you are on the right track.

One of the issues with 'air drying' is the water evaporates off but the GUNK is left behind. It's kinda like smearing mud around without removing the mud.

A towel dry is a better option for low-gloss floors. It ensures you get the water AND the gunk off (the stuff you were trying to clean in the first place).