Hi Jen, yes, that is a Choke-A-Matic, as you say. Just one thing: when you set the speed control as far as it will go to maximum, and the choke handle is pulled out, that closes the choke, it doesn't open it. Immediately after the engine fires, you must pull the speed control back far enough for the choke to be pushed all the way in, which is the open position, suitable for actually running the engine. Do you begin to see why there was stuff running out of the carburetor when you kept pulling the starter with the choke fully closed? That will have flooded the carburetor. With that nasty Choke-A-Matic unit, you have to be very quick in opening the choke after the engine fires, or it rich-loads and stalls. Then you have to restart it with the choke open, and all is well.

Also, now that I actually look at the engine instead of the IPL, it has a plastic boot over the top of the spark plug, so it can't have the old flip-lever kill switch. That means it must have a kill switch in the governor plate mechanism, since it doesn't have the one shown in the IPL. Lack of spark on Briggs engines is frequently due to a malfunction of that kill switch. Hence you need to sort that out, if the spark test shows no spark. Remember though, because you have a kill switch, whenever the speed control is set to minimum speed (the opposite end of the range to the end where it closes the choke), the kill switch operates automatically, so there will be no spark. So, test for spark with the speed control in the middle of its movement range, or if you prefer, at the choke position: stay away from the slow speed position. Please do the spark test, and if there is no spark, we'll need some pictures of the kill switch area. I'll get to that in a moment, but meanwhile you should bear in mind that your engine was made in 1973 and hence has a breaker-points-and-condenser ignition system: electronic ignition was not introduced until 1982. Here is what you are up against:
[Linked Image]

Don't despair, even if there is a problem in there, it probably won't be hard to fix, and if it is, you just fit a Magnetron electronic ignition unit: it is fully interchangeable.

Here is a not-very-clear illustration of the kill switch on your engine (that is, an early version of the Pulsa-Jet carburetor with Choke-A-Matic):
[Linked Image]

Here is one of your pictures, cropped and with the kill switch circled in green:
[Linked Image]

So, if your engine fails the spark test, we will need some detailed pictures of the mysterious object labelled "STOP SWITCH" in Figure 52, and circled in the above picture.