Chainsaw Repair

Not a big deal to replace a plug wire. You will have to remove the starter and coil to do it, then reset the coil to flywheel gap. IIRC gap should be 0.3mm a business card will get you close. Not unusual for plug wires to cook up a bit if they come in contact with the cylinder, that is what the insulation tube in your picture is for.

OMO but it looks like the plug wire has been changed before, the plug boot does not look to be factory. It is hard to see but it also appears that the plug clip was not properly attached to the wire. Look at the attached picture. When HVA attaches the clip to the wire they punch a hole through the wire, then insert the bent end of the clip through the wire and close the bend against the wire.