Acrylic Platters and Shinny Spots

This matt finish is a secondary step, it's like a coating that is applied.
Do not use Windex, that is the worst thing to use on acrylic. Can cause grazing eventually.
Leave it alone, like McDonald 43 mentioned, it's the oil in yours hands that is showing up. Just wipe with dry soft cloth.

Windex contains Alcohol. I don't mean to be a know it all but after 40 years in the Plastic ( Acrylic ) business I think I have some idea of what I am talking about.
Denatured Alcohol is fine but not products with Alcohol. The process of the frosted finish is done in two ways. It is applied by a spray gun with a Dupont Matt based material. The other way is Sand Blasting. When sand blasted and there is not a sealer coat put on it is the oil in your hands that impregnants the Acrylic. This will cause those shiny areas.
You can use any cleaner without Alcohol content. The best cleaner is Novus # 1 for any plastic ( Acrylic )
When I mentioned grazing can or will appear, it will, it's just a matter of time if Alcohol is used.
I am sure there are cleaners on the open market that can be used I just don't know for sure which ones they are.

Markd51 Novus #1 is a cleaner only and also eliminates static. Your might be thinking of Novus #2 which is a scratch remover. We use Denatured everyday of the week to help clean acrylic that may have a residue left on it.