That's a lot of miles for a LIKE200i in N. America!
Would likely win 1st prize here on the forum, I think.
You are on the edge of the unknown here - we have little experience with 14,000 mile LIKE's, and do not know how long these bikes will last.
Only a few have reported mileage approaching your scoot's.....but that is because so few put many miles on any small scooter in this country. Not the scooter's fault.
Look it over, ask for service records (oil changes and valves adjusted !?!) A good set of tires runs @ $150/$200 installed.
Ride it. Good pulling power? Leaks under engine, under CVT cover, around back wheel hub?
If it rides good, and sounds good today - then I would think you will get many more good running miles out of it.
If tires are funky might try an offer of $700 - but think $800 is a fair price for a good running LIKE200i.
Walk away if it's not a good runner and in decent shape (check parts prices if things look like they will need to be replaced.
http://www.kymcopartsmonster.com/p/Kymco-Scooter-Parts)
Good luck
Stig