I can see this saw blade being used in like ripping operations. Its hard to picture...and this is 100% speculation, but I can see a tablesaw being equipped with these blades. The square blade would rotate with the four corners using the teeth to cut through the wood and then the middle of the blade "sweeping" out the swarf (sawdust). That would certainly explain why the teeth on the corners are shaped for a shearing cut, and the middle ones are rather straight to clean out the kerf better.
The thing to keep in mind is, these old tablesaws (or buzz saws as they were called) were beefy units with lots of cast iron for mass. They could easily handle something out of round and still not vibrate like a saw that was made today would. They also had flat leather belts so if something was hit to hard, the belt would slip long before anything broke...and speeds on these old flat belted monsters could be changed with a simple move of the cone pulleys. You could easily speed up or slow down the saw to be able to saw whatever it is you wanted...or in this case, mount whatever sawblade you wanted on it...even if it was squarish.
Again this is all just speculation
I have no intention of traveling from birth to the grave in a manicured and well preserved body; but rather I will skid in sideways, totally beat up, completely worn out, utterly exhausted and jump off my tractor and loudly yell, "Wow, this is what it took to feed a nation!"