Modern ones will. The gpu requirement is basically says any gpu from 2011 and newer (2011 was gcn 1.0 and kepler) with Vulkan support.
For windows, vulkan is supported by skylake(6th gen) and newer, for linux, vulkan is supported all the way back to Ivy Bridge, but the experience playing CSGO would probably be terrible.
One thing to note for linux and GCN GPUs, is that older GCN based cards doesn't use AMDGPU driver out of the box, so vulkan won't work initially. You need a kernel parameter to enable amdgpu for older GCN (at least I've had to do that with arch linux). But when it is enabled it works great in my experience. You will get a warning in the console that the support for that GPU is experimental though.
Also vulkan support for Ivy Bridge is not complete and is experimental. It is unfortunately not possible to use DXVK on ivy bridge due to this.
Finally a game my gtx 980ti can officially run! It's been a long time since I've seen that , but it still runs most stuff just fine. Quite a little trooper, that card 🙂
Try running the Windows version through Proton instead. You can do that by forcing a Proton version, and it will download the Windows version.
This worked extremely well for me with an 8x performance boost in Bioshock Infinite because their Linux build runs on an old version of OpenGL and old libs, while proton translates DX11 into Vulkan.