check the valves. if the valves are adjusted wrong it could do that. also I had an engine one that just didn't have valve rockers. they just weren't there. stole some off another engine and it ran fine. so I would check my valve lash if I were you. and also try starting it on either.
Agree with Karts of Kaos. Most small engines have what's called a compression release feature. It's a "lever" on the camshaft that cracks open the exhaust valve slightly on initial starts to allow the rope to be pulled easier. If the exhaust valve isn't adjusted correctly it may not allow the release mechanism to work properly. Something else to check is the coil wire or plug boot for cracks. I picked up a used kart with a 212 Predator engine on it, seller was able to start it but it ran real rough and the engine shook terribly. After checking the flywheel key, valve adjustment, removing the cam to check the release mechanism and removing the valves to see if they were bent, it ends up the plug boot was broken and was shorting out. Couldn't see it, there was electrical tape on the boot that looked factory at first. Peeled the tape off and the boot fell apart.