My Mayfair is the same model. I think Norm is right that these are actually 125CC. Mine definitely has the clips and was often widely touted to be a 160CC as it takes the much larger fishtail muffler, that was at least designed to handle 160CC. You have purchased the correct aftermarket muffler. Pity you couldn't find an old fishtail type. They come up on ebay from time to time.
You can see the cut out on the engine block fins in your photo and the holes, which means your engine requires muffler clips. Yours is missing the two rods that go through those holes and then you will also need clips to help hold the muffler on. The rods fasten in place with some circlips, but I have seen people use the same diameter threaded rod, which works okay. You can buy the muffler clips cheaply from any online mower place, but make sure you get the right ones for that muffler. You will require the wavy shaped clips, not the straight ones. The straight ones are for later Power Torque models, 1984 onwards.
Gaskets for your muffler are dime a dozen on ebay.
