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no, he's cut it in the horizontal to stop the legs flexing when you're planing (for example) which exerts horizontal forces along the top of the bench. the dado (properly called a groove in the UK) is for sturdiness, not to support the cross member. the screws are more than enough to keep it from dropping off(!)
I'd use the design from YT nerd and general weird genius matthias wandel
it's designed for minimal tools. you don't even need the circ saw if you're careful with a hand saw
https://youtu.be/M_xJD_aylYw
it's not the same level of insanely heavy sturdy that lots of people build, but it's the best beginner design ive come across