Here's a clickable link to the page:
These sorts of projects are not covered by any enforceable codes or standards. It's not premises wiring, so the NEC doesn't apply. UL, ETL, and other private testing organizations only deal with products in commerce, not one-off devices made for your own use. You can make whatever you want for fun, safe or not. It's a free country!
The only major red flag I see for safety is the lack of grounding. You really need to connect all the ground terminals of the receptacles to the incoming grounding wire of the cord. With that said, I've been building stuff like that my whole life and I can see a few things I'd do differently. I don't think there's anything super dangerous about it as-is, but it's not assembled the way someone would likely choose to assemble it if they had much experience with this kind of wiring. These are the changes I'd make:
1: Don't use the back-stab holes on the receptacles. Get high quality receptacles with back-wired screw terminals, not spring loaded back-stab holes. Those are notoriously unreliable. It is an NEC violation to use them to pass a neutral connection through a receptacle as shown here. It's hardly any more difficult to do it the right way using nice stranded wire and good screw-down connections.
2: Use larger wire for all power connections. In applications like this, it is common to use much smaller wire for a given amperage than would be used in wiring a building. That's fine, but don't take it too far. Those are 10A relays, and #18 is pretty light for that. Even #16 would probably be fine. Remember that you may have this plugged into a 20A circuit, but you are limited to 10A per receptacle by the relay ratings and you may be limited to less than 20A total by the choice of cord and internal wiring that you use.
3: Do a better job handling the connections to the relays. All those orange wires are a mess, and unnecessary. I'd take a single piece of #14 or #16 stranded wire, and strip a 1/2" section every 3", in 7 places. Fold each stripped section in half, and insert into the relay terminals. Connect one end to the last relay, and the other end to your incoming power. Now you have a single wire connecting one terminal of each relay together to supply power. Much cleaner.
4: I would assemble the whole thing in a better enclosure. A Cantex box is cheap, tough, and available at Lowes or Home Depot. A purpose-built electronic enclosure might provide more options for internal mounting of the electronics, but at a higher price and you'd have to order it.
5: I would consider using solid-state relays instead of mechanical ones. It's an upgrade. It adds the requirement of dealing with cooling, but they last much longer and are silent.
6: Pay attention to the comments section on that Instructables post. There seem to be some issues on the software and digital hardware side of things, which I did not address at all.