I'm not sure what this joint is even called
In English terminology this is a dowel-reinforced mitred rebate joint (US English substitute rabbet for rebate). It is not an easy joint to form on powered equipment (fairly challenging to form by hand as well!) if you want it dead accurate, which it needs to be to work at all.
The basic joint, without the dowels, gives the neat corner appearance of a mitre joint but adds long-grain glue surfaces to improve the strength of the glue bond. But the dowels alone strengthen the joint. So actually there's no point in going to the trouble of creating this joint for strength purposes.
I'd suggest only doing it if you want the challenge, or you want to show off the joint on an exposed edge in the finished piece (e.g. the front of a bookcase or the corner joints on a jewellery box).
As an alternative I would recommend this joint instead, the lock-mitre:
Source: Lock-Mitre on Canadian Woodworking.
If anything it's more attractive, as the name suggests it self-locks which helps to remove the need for dowels, and as you can see from the picture it is much more easily formed since you use the one router bit (and the one setup on the router table) for both end profiles.
Tip: if you want to go ahead with trying the joint you posted, drill the dowel holes before shaping the edges of the boards. Possibly not obvious but it's much easier to drill those accurately when your edges are still square. Also, drill the holes that go into the end grain slightly deeper than needed so that there's no possibility of the dowels bottoming out, which would prevent the joint from closing up.
Not part of what you asked about but I wanted to touch on it anyway.
He used a compound miter saw, but ours doesn't tilt.
You can still do this cut using a standard mitre saw for stock that isn't too wide.
You set up a temporary fence at exactly 45°, clamp it well so it can't move (with the clamps safely positioned so they don't foul the saw body and the blade), then run the saw once to trim the fence to length. Then it's just a matter of holding your workpieces upright against the fence to get accurate, repeatable edge-mitre cuts.