Welcome to the forum.
There was no link showing the part that would be fit into your mower, but it should be fine.
There are two ways that convert a 21" Snapper Hi Vac into a recycling Ninja mower. One is using a plug in the chute, retained by the (unused) bag. The other is to remove / replace the chute w/ a recycling plate.
Both the plug and the plate are shown in this image. The side discharge is also shown.