How do you built the tounges?
The tongues can be cut a bunch of different ways. The first three that come to mind, in no particular order:
1) Use a table saw with a dado stack to cut one full-width tongue, then use a handsaw (or jigsaw) to make them look like the ones in the video. If necessary, clean up with a file.
2) Use a router to cut the full width tongue, then use a handsaw, jigsaw, or router to make them look like the ones in the video.
3) Use a rabbet plane (Stanley #78 or equivalent) to cut the full width tongue, etc.
Short version, you want a tenon that's long in a few places and short everywhere else. Use some tool to cut it to the long length everywhere, then remove material between them. The mortise can be cut with a plow plane, a router, or a table saw. I tend towards hand tools where possible, so I'd go with a rabbet plane, handsaw, plow plane, and chisel for my toolset. That's not fastest way by any stretch (I'm pretty sure the router wins for speed), but I prefer the quiet.