How to convert this recipe to a 8" round cake pan.

I find it best when changing pan sizes, particularly with cakes, that it's best to keep the depth close to the same, both to preserve the character of the cake and it's baking characteristics. In this case I would multiply the recipe by 1 1/2 to go from one 9" to two 8" layers. These figures can be rounded pretty casually, baking isn't all THAT exact an art. In this case it would multiply out to X1.580246914- assuming that the pan's were exactly their nominal size, which they're often not, but you really don't need to cut it that fine.

Have a look at one of the many charts out there which provide volume estimates of baking pans, which help navigate between recipes as written and pans we want or need to use. For example:
https://www.joyofbaking.com/PanSizes.html
The recipe itself suggests one full recipe can be baked either in a 9x2" pan or two smaller pans (like your two 8" diameter ones).
Just start checking sooner than usual for doneness.