That's more or less the way it looks to me. If I were you, at this point I'd be removing the cylinder head and taking a look at the top of the piston.
Here is the page in the B&S engine overhaul manual:
http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_150.htmYou can learn more by using the "back" and "next" buttons on the top of the pages. You might like to read ahead a bit, and always check the manual before you do something to your engine.
The first step will be to remove the air cowl, to expose the cylinder head. It is secured by four small hex-head screws. Then the cylinder head is held by 8 hex-head bolts, of two different lengths. The long ones have to go back into the long-thread holes when you finish the job. As soon as you have the head off we'd all like to see pictures of the top of the piston, and the underside of the cylinder head.
Incidentally if the piston is broken, something unusual must have happened to cause it. One of my interminable anecdotes: I had an OHV Morris Minor long ago in my youth, and I was driving it one night when a rattle suddenly developed in the engine, and almost simultaneously one cylinder stopped firing. I declutched and switched off in less than 5 seconds, probably a lot less, and rather dolefully towed it home. Next morning I removed the cylinder head. Things were much better than I expected. All that had happened is that a nut welded to the inside of the oil-bath air cleaner had come unwelded and dropped through the manifold, past the inlet valve, into the cylinder. It had immediately hit the side-electrode of the spark plug, closing up the gap and stopping it from firing. I discarded the nut, regapped the plug, and put the head back on, even re-using the same copper-asbestos head gasket. Adjusted the tappet clearances, and drove away no worse off. If it had taken a bit longer to hit the ignition switch, however ... At the time I thought it had probably dropped a valve and smashed a piston, so I was a happy lad.
