It literally says "32 bit RISC-V homemade CPU out of discrete components".

I dont know how you would stretch the definition of cpu in form of discrete components but yea current processors also stray from the definition of a alu and a control unit and registers since people call the different cores cpus. But even a Mikrocontroller has a all that.

You need a cpu to run linux. If you just want to rin a "program" you can do that with logic gates and no alu or control unit but that would limit the form of your program to exactly that circuit.