Yes that would to replace the points. I use that universal ignitor on Kawasaki engines when their ignitors goes bad. It is also usable on the old cast iron crankcase version of the Briggs engine that have positive ground ignition systems.
But OP was refer to the HT (high tension lead , plug wire) being broken off. I said those are replaceable if the OP is resourceful enough. There are however some very old coils that you simply can't replace the HT lead due to design.
Tyler is right that most of the 2 to 4 hp Briggs engines used the same Magnetron coil and here there are tons of them sitting in scrape piles. They are mostly there because the mower owners were unwilling to pay for repairs needed and had opted for new mowers instead.
I can't even sell a repaired unit as most buyers are demanding for me to sell then for under $20 because they can go to any yard sale and pick them for that. To me there is a lot of difference between a good working mower and one that was cobbled up.
