For a 'kinda' match you can probably just determine the type of veneer on the top (sort of looks like maple from here but I could be way off) strip the current top, get some veneer to match the specie and general color of the stripped wood then make your own insert and veneer it. If you wanted to have a dead on match you could re-veneer the whole table from one piece (or even use very thin cabinet grade plywood) and redo the current top rather than refinishing it.
I'd probably just find something else to sit there when the machine wasn't in residence
