Cleaning dried up hand-disinfectant from lacquered wood floor
I think you're going to have to sand and refinish the floor, or at least a portion of it.  

Hand sanitizer contains a high concentration of alcohol which is a good solvent for many types of wood coatings inclulding lacquer. The portions that appear white look as though some or all of the finish has been cleaned off.  No additional "removal" is going to remove that since the problem is that the finish has been removed.

With a floor like this you may be able to sand and refinish only a section by using the natural lines and different wood tones to your advantage to choose an area that can be refinished vs. doing the entire floor.