Linux OpenSuse Leap 42.1 Gnome and Crossover 16.0.1. Origin installer now requires windows 7, but will not start in windows 7 mode. In windows xp 32 bit mode, it will refuse to install because it wants windows 7. As suggested on Wine AppDB by user mikaelvz, you have to grab the legacy origin installer from https://www.dm.origin.com/download/legacy
And as suggested by user Dylan Morisson (wine appdb too), you will have to install a virtual machine software in window xp 32 bits mode and install and run the legacy origin installer from there. Start origin once, disable "Origin In game" in the application settings, and after that you will grab all the origin folder from the windows xp 32 bit VM to the crossover windows xp 32 bit bottle with a legacy origin half-installed (because it will not install fully there) and overwrite, then it will work, you will have a fully installed legacy origin.
I used Virtual Box for a virtual machine. It required guest additionals, which can be installed from the software menu itself. It also required "sudo modprobe vboxdrv", adding the linux session user to the vbox group and restarting, and of course a windows xp 32 bit iso image. Then you will be able to create a shared folder to exchange the files between the Virtual machine and opensuse. It was not needed to setup internet connection on the VM.
You have to disable the "Origin in Game" because otherwise your games will crash at startup (never solved bug). After a game is installed it will attempt to show a "Install complete!" notification, but it will fail and crash Origin, but worry not, your game was installed, restart. I saw an issue at wine only (not crossover anymore) if I remember it right, Origin will crash at login because of the first bug said above, to workaround that I had to replace igo32.dll, igo64.dll and igoproxy64.dll with ones from a previous and "startable" Origin version, then I just did the workaround for the first bug above, at wine it was needed to install corefonts using winetricks, but Crossover does that automatically anyway.