A few years ago I considered trying to build a simple 32-bit RISC processor out of 74xx series logic chips. I had just taken parts 1 and 3 of the the MITx MOOC 6.004x, "Computation Structures".
Part 1 covered CMOS, combinatorial logic, sequential logic, FSMs and stuff like that, and performance considerations, and culminated with designing a 32-bit ALU, which did add, sub, all 16 logic ops, compares, and shifts (logical or arithmetic) of 0 to 31 bits in either direction.
In part 2 the students design a 32-bit processor and implement it in the simulator. The design is all at the gate level, except we were given two things as black boxes: (1) a register file of 32 32-bit registers, and (2) a ROM with 64 18-bit words.
Part 3 adds caching and other performance.
Here was the parts list I came up with for my design, not counting whatever it would have to do the 32x32 register file and the 64x18 ROM. In the follows the name of a logic element (NOR, MUX, etc) followed by a number means an element with that number of inputs. E.g, NOR2 is a 2 input NOT gate, and MUX4 is a 4 input multiplexor. DREG is something that can store 1 bit, which would probably be a D flip flop.
The parts list:
295 AND2
8 AND3
32 DREG
3 NOR2
4 OR2
96 OR3
20 OR4
226 XOR2
6 NOT
563 MUX2
161 MUX4
That came out to around 350 chips. My biggest breadboard could hold about 32 chips, so I'd need around 11 or 12 of those, plus whatever more would be needed for the register file and ROM.
353 of those 563 MUX2s are in the shifter in the ALU, which can handle left or right arithmetic or logical shift by 0 to 31 in one clock cycle. If I added a new instruction that just does a logic right shift by 1 and made the old shift instructions all trap so they can be handled in software that would get rid of most of those 353 MUX2s.
That would cut the chip count to around 270. That was still more than I was willing to deal with so that was the end of that.
Given that with a PCB instead of a breadboard you'd get higher density, I think mine would have easily fit (even with the full shifter) in the amount of space that it looks like they are using with plenty left over, if I'm estimating the size of their boards right from the photos, so I don't see anything obviously implausible about their project.