I agree that a 48" table doesn't seat more than 6 players comfortably. I built a 54" round to fit 8 more comfortably, which meant I had to find 5' x 5' plywood, not usually sold at a the Lowes Depot type places. There was a lumber place nearby though that had the 5' stuff in 3/4 thickness, so I got lucky there.
Couple things I'd say after watching the video -
1) finding the center is more easily and accurately done by making a mark from the corners diagonally, instead of the edges of the wood. You can see it on the pic below from my build. Also, a router with a circle jig is a much cleaner and exact tool than a jigsaw. If you want a racetrack, use a router with jig for a cleaner cut. I'd recommend a 1/4 shank bit for tables with a racetrack. With a router and a pattern bit you can also make exact copies of the circles and other pieces.
2) No overhang of the 1/4 foam for the playing surface, which it looks like they have in the video. Cut the playing surface foam flush to the wood. An electric knife works really well for cutting foam.
Here's a cross section of my table, not showing cup holder rings.