The only thing I would trust is BRASSO, but if the chrome plating is thin (very likely) then care with ANY product is needed to avoid plishing the thin chrome away to the nickel housing (or plastic housing if it's only a chrome effect on plastic)
As an example, similar minor scratches on my spectacle lenses have been removed using brasso.
But, since we don't know if it really is chrome or (more likely) just a plastic chrome effect, care with anything is needed to polish. Personally, I would consider that the chances of making it worse would be higher than those of eliminating the scratches, and would simply leave well alone. It's only an audio player. It's only a sign of use.