It looks like 40 x 40 mm extrusion, but I think you'll be able to make it in 30 mm.
I would use a nice Festool grey or blue particle board and try the same material for the drawers. The drawer slides can be screwed into the extrusion with adjustable nuts. I would also use simple slides, since I guess the ones used in the video or specifically for extrusions are much more expensive.
Of course there's the question of how to hold the drawers in when you tilt the cart to the front, without any safety lock I would be a little nervous.
