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Formica can be coated with many paints or clear finishes as long as it is absolutely clean and is very slightly sanded... 220 grit paper would be the roughest that should be used.
Since you want to maintain the appearance but just lower the gloss, you could try a water-based polyacrylic coating. This is a durable, abrasion resistant product that should serve your purposes. Minwax is one manufacturer of this product. Apply it with a foam brush or lint-free roller... very lightly! Multiple coats are preferable to a single heavy coat. This product can also be sprayed if you have access to the proper equipment. For a small area, though, spraying is unnecessary to obtain a smooth finish.
Thorough stirring is essential. These products are naturally glossy... additives are used to produce the satin or "matte" effect. Don't stir too vigorously and don't shake the can... the bubbles caused by shaking may not "pop" fully before the finish dries leaving you with a rough finish. Sand lightly between coats with 220 grit sandpaper. Do not use steelwool.
This is not a manufacturer-approved use for this product, so don't expect to find it listed on the can. However, the water-based polyacrylic products are recommended for use over old finishes including polyurethane… provided that the surface has not been waxed or treated with an oily finish or soap. Hence, you should get good adhesion on a plastic laminate.