Wouldn't it be much easier to "vertex only"-bevel a basic icosphere and then bevel the resulting edges normally rather than connecting roughly 200 triangles for each individual face?
Just for curiosity, I have tried this and it looks like it could work too.
I start with a basic icosphere (only 2 subdivisions). I select every vertex and I bevel but in edge mode (not vertex mode like it suggested).
The geometry gets pretty messed up but it can be fixed next with a Merge by distance and tweaking a bit the threshold.
It looks like you get a pretty basic "soccer ball".
Anyways, If you keep doing the following steps (beveling the edges and so on), you don't end up with the exact same geometry as the one showed in the video.
Maybe you can keep beveling and doing the extrude+Scale thingy, but the geometry is not exactly identical.
And since I'm a beginner that is the farthest I get by myself. Once I start trying to smooth, subdivide or whatever I start getting weird results lol
