It looks thick, therefore high build, and all the colour's in the polish meaning the wood itself isn't dyed and/or stained before polish has been applied. Based on that reading, one candidate for the polish type is old fashioned nitro-cellulose lacquer with dye added (aka toning) to build up the colour. My suggestion of polish type could be all wet, so treat it as no more than a best guess.
Best option is likely to be strip and refinish, unless you have specialised skills and kit. The fact that you asked your question suggests you may be a bit short of either the skills or the kit, or perhaps both - no insult intended. Slainte.