Sadly it seems like Insurgency: Sandstorm is not one you'll be enjoying on the Linux desktop or Valve's Steam Deck any time soon, even with Epic Games supporting Easy Anti-Cheat with Wine / Proton.
A game that originally planned Linux support, which New World Interactive decided not to do while also cancelling the planned story campaign back in 2019. The last hope was Steam Play Proton but it appears the developer will not be enabling support for it in EAC.
Writing in their recent patch notes, the developer said this:
The Linux Situation
Hello penguin pals, this message is being written for you by someone who has in their lifetime been a self-described Linux-head. Yes, we are very much aware that EAC announced Proton and Wine compatibility. Please understand however that we would still need to do quite a bit of development work to properly support Linux, and at this point in time we do not have that capacity. Thank you for your understanding!
Perhaps they, like we expect others to, may change their mind once the Steam Deck is out and they might see more players asking them to support it. That, or people just go elsewhere and find a different game. I'm sure there will eventually be no shortage of first-person shooters that you will be able to play online.