Valve has spent the last 3+ years working on their Proton software which allows Steam games designed for Windows to effortlessly run on Linux out of the box. Valve is also releasing their new Steam Deck console which will be running GNU/Linux, not Windows. ArmA III even works great using Proton, except you can't connect to BattlEye enabled servers.

In fact, most Steam games are supported out of the box on Linux through Proton with the notable exception of games that use heavy anticheat software such as EAC or BattlEye. However, Valve has been working with the anticheat companies as well, and as of recent EAC and BattlEye are supported on Proton in an opt-in basis.

BattlEye on Twitter : BattlEye has provided native Linux and Mac support for a long time and we can announce that we will also support the upcoming Steam Deck (Proton). This will be done on an opt-in basis with game developers

Going forward, the only thing Bohemia Interactive would need to do to enable Proton BattlEye support for their games is to contact BattlEye and request it, as explained by Valve in their post here:

Update on BattlEye + Proton support : As we mentioned previously, BattlEye on Proton integration has reached a point where all a developer needs to do is reach out BattlEye to enable it for their title. No additional work is required by the developer besides that communication. Partners have started turning on BattlEye support for their titles, meaning these games are now working on Steam Deck.

So please Bohemia Interactive, contact BattlEye to enable Proton support for DayZ and ArmA III so all your patient GNU/Linux users who have supported you for years can finally play the game natively, as well as so your games can run without issues on the new Steam Deck console.