It wants to install itself into C:\Program Files\Electronic Arts\EA Desktop and access the game at their location and your user would need to have permission for your apps to do that.
I imagine there could be some way to get it to work by getting the applications installed in locations you have more access to, like the desktop, but not really something I have had the need to test out.
As for EA Games on Steam requiring Origin that's for the games that arrived on Origin only and then later got on Steam, I believe all newer games that arrive on both at launch wont need Origin/EA Desktop but just need to have the Steam account connected to the EA Account.
