The valve stem is worn out probably. Try measuring with a micrometer at place where the valve guide rides and near the end of the stem, where there is no wear. You can measure the diameter of the valve guides with a series of # drills. I agree with Laitch, the play is excessive.
Changing valve guides is repair shop territory: warming up the head in a control temperature oven (not over your kitchen range), driving the old guide out without banging anything else, driving the new guide all the way to the spec height w/o misalignment, and then, machining the seat to have it concentric with the new guide, and shaving it to spec width. Not impossible, but requires practice, and a lot of special tools.
I agree that the price of an exhaust valve is exorbitant, but for an exhaust ventile, might not be :(
Curious: how many miles in this bike; for the wear of the valve seal surface, a lot.