Existing PS4 player has to buy a PC copy?

[Saccharin]

So my friend is a PS4 player but they got sick of the PSN maintenance screwing with their game time, so they downloaded the PC version client off the website and put in their details in the launcher and now it's asking for a registration code. Since they just downloaded the client off the site they don't have a registration code. So to play on PC do they have to buy a new copy of the game for PC?

You do. This is likely a restriction placed by Sony rather than SE.