For something simpler than the computer described in the article, you might be interested in Usagi Electric's UE-1 vacuum tube computer. Construction is nearing completion, and it's documented on Youtube:
Yes, code executes directly from a literal loop of paper tape, and more specifically, there is only one loop (the paper tape loop), and every instructions executes at every iteration.
Yet it can do what any other computer can do (in terms of computation, not I/O), because not every instruction has to actually effectively do something in each iteration, and it is a cornerstone of theoretical computer science that you can transform every program into one represented in an academic language called "WHILE", which is restricted to exactly that principle: It only consists of a single outer WHILE loop, and then inside the loop you have a bunch of conditions.
https://www.youtube.com/playlist?list=PLnw98JPyObn0v-98gRV9P...
This is a 1-bit design based on the Motorola MC14500B:
https://en.wikipedia.org/wiki/Motorola_MC14500B
Code executes directly from a literal loop of paper tape, so the clock speed is very slow. I expect this design would also work with relay logic.