The engine was manufactured on 3 March 1980, in Briggs' Rolla, Missouri engine plant. Because it was made before 1982, it has a breaker points ignition system. You may wish to consider fitting the later electronic ignition module (called Magnetron) which eliminates the points and condenser. You can probably obtain either the old or new unit second-hand by posting details in the Outdoorking Wanted forum.

Here is the Illustrated Parts List:
http://bsintek.basco.com/BriggsDocumentDisplay/Z6jmyBVJ1DajI.pdf

Here is the Operator's Manual:
http://bsintek.basco.com/BriggsDocumentDisplay/flivAJX-nfBhU7y.pdf

You will see that the part number of the original coil is 298502 (the reference number on the exploded diagram is 333, and you will find the corresponding part number on page 24 of 28. Your Type No. is not one of those listed as requiring coil p/n 298274).