Game has no audio whatsoever. Totally silent.

As far as you are aware, are you using bare ALSA, or PulseAudio?
With plain ALSA, I am able to run the game (version 1.190) without any audio abnormalities.

For the purpose of obtaining important textual information, within your preferred terminal emulator, have you attempted to directly run the executable?

Example:
[path to Atom RPG directory]/game/AtomRPG.x86_64

I just did that same result.

For the sake of clarity: I had not suggested that the audio issue would be rectified by directly running the executable (via your terminal emulator of choice). Rather, it had been intended to be used as a method for (potentially) gathering details about the problem (from generated error messages).

Within the following text file, is there any mention of audio-specific errors (may mention ALSA or PulseAudio)?
"$HOME/.config/unity3d/AtomTeam/Atom/Player.log"

Apologies, despite using linux I'm not really educated about how it works.
Ctrl+f doesn't reveal anything in that file about audio, pulse, or ALSA.
The term ERROR came up a couple times, but it was all stuff related to shaders. I'm assuming those errors aren't all that important since I encounter no graphical glitches.