Dull the surface of the floor tiles as much as possible with a belt sander. It won’t sand the existing gloss completely off but can diminish the sheen. Don’t sand the lines of grout between the tiles.
Vacuum up the dust.
Apply oil-based polyurethane gloss over the tile surface, starting at the wall farthest from the doorway so you can work your way out. Make all the brush strokes go in the same direction on each tile. Don’t get it on the grout lines. Allow the polyurethane to dry for 24 hours.
Hand-sand the polyurethane with fine sandpaper, using quick, light strokes to dull the shine. Wipe off the dust.
Brush on a second layer of polyurethane in the same manner as the first. Let it dry 24 hours. Sand it lightly by hand. Apply a third layer. Let the third layer dry for 24 hours.