23913 just means he created too many console entrys on Wiimmfi. Waiting 24 hours (without trying to go online and without creating more consoles) should fix that.

Although "creating a console" sounds a lot like a Wiimmfi NAND generator in Dolphin which really shouldn't be used. It is recommended to use a real Wii's NAND in Dolphin, as outlined here: de.dolphin-emu.org/docs/guides/nand-usage-guide/

And between "Sunday" and now, has there been a continuous 24-hour-period without him trying to go online and without opening the .exe file? I'm not sure if more access attempts (with possibly new consoles) during that time reset the timer or not.

Can you tell me what tutorial he used so I can check what this mysterious exe file is?

To check any server logs, I'd need any piece of identifying information. With these NAND generators that is a bit tricky (one of the reasons they're not recommended)...
Does he have a (semi-)static IP and can you get his public IP address, then I could check the login logs on the server.

Then can you get his current public IP (with which he just tried to login) so I can check the logs?

Thanks. I don't know (yet) what this Wiimmfi enabler thing does, but apparently it does not do its job properly.

He needs to follow this tutorial -> de.dolphin-emu.org/docs/guides/nand-usage-guide/ -> to get a real Wii's NAND into his Dolphin, because his Dolphin is creating a new console identity with every login try.

EDIT: And I would also recommend deleting his whole Dolphin config folder (if he doesn't have important savegames or something else in it), let Dolphin recreate it freshly, *then* use the above tutorial using a NAND from his actual Wii, and not using this "Wiimmfi enabler" (which I have looked at just now, it tries to be "smart" and get people online without an actual NAND, but apparently that didn't work).