How to lightly dull the sheen of latex acrylic paint touchups

I wouldn't try to scrape off the messed up area while it's wet because you'll leave ridges at the edges of the area, which will look even worse. Leave the area to dry before trying to fix it.

To get it to dry quickly, higher temperatures and low humidity are your friends. I've used a space heater and an oscillating fan when I needed paint dried quickly: arrange the heater and the fan so that warm air gets blown past the work piece continually. Leave it running overnight: it looks like you're using a higher-gloss paint, which will form a skin quickly, but underneath will remain wet for a while.

(See here for a technique for removing drip marks.)

This E-How article says that a soak with your normal shampoo, followed by running a fine-tooth comb through the affected area(s), should remove water-based paints including latex acrylic. By fine-tooth, I assume they mean a comb like a pocket or dressing table comb, but you may have more luck with something like a lice comb.

Now, latex paint with VOCs may cause other types of discoloration, similar to thinners (which is why you NEVER put paint thinner on your hair; no turpentine, no acetone, no methylated spirits, no nothing). Also, certain dyes, like red and orange, will soak into surfaces (even some things you wouldn't consider "porous", like ceramic tile) and become extremely difficult to remove. I dunno what color you painted the closet or exactly what type of paint you used, but it may not be a layer of actual paint causing the discoloration anymore.