There's really not a minimum or preferred specs anymore. If your laptop/PC can run a browser (Chrome, for example), it should be able to run The Tournament Director. The beefier your computer (more memory, faster processor mainly) the smoother and more responsive the TD will be.
That said, I still use and do most development work on my desktop PC with an i7-2600 (3.4GHz) in it and 16GB of memory. Yes, it's an i7 but it's gen 2 from 2011! I have now used the same desktop for over 10 years. If I were shopping today I would probably try to get an i5 at least and 16GB of memory at a minimum, budget allowing. There are so many processors and variants, just in the Intel family, not to mention other manufacturers, it's overwhelming. And also difficult to know if an i5 from today would be faster and more efficient than my i7 from 10 years ago. I feel 8GB is probably enough, but personally I would shoot for at least 16GB, if for nothing else than to future proof just a bit.
I have a "work" laptop that has an i7-8650U (1.9GHz) in it and 32GB of memory. My old desktop still outperforms it, but I believe the processors are meant for different computing environments (one's desktop, one's mobile and built for more power efficiency). The work laptop also has a LOT of security software on it that undoubtedly slows it considerably.
So I think any fairly recent CPU with a minimum amount of memory (8GB but 16GB would be better) should handle the TD just fine.