Hey @MichaelEmerald ,
got hit by the 1-day-post-limit yesterday while “spamming” the forum a bit for good! 
So, let me help sorting things out a bit.
01.) I would agree when you say, something that happens with an application on one system but not another is most likely related to that specific system! However, sadly in IT there are THAT MUCH variables always around an issue, that there is plenty of possible causes left. Alone that one needs to not forget obvious things like cables and what not, especially with PC audio issues, can drive you mad! 
02.) FxSound is installed as a sound device like any other like a discrete sound card, your motherboards sound-chip and so forth. This is the basis. It normally then sits between your real audio device and the applications playing audio and does its magic “in the middle”. When you disable the FxSound sound device, of course everything else related to it is also gone; this can be compared to removing a sound card from the system or at least unistalling its driver so it could not be used anymore. This is the driver/device part of it. The FxSound application then simply is the so-called “frontend” or user interface where you set everything to your liking. Maybe it helps when separating things so far and explaning a bit (not knowing how technically experienced you are).
03.) Since you can fix it with simply re-enabling the audio device and restarting the app could point at a cause with FxSound itself - or not! When you have a more “exotic” cause like an imcompatibility with your soundcard or such, this already explains why it happens on system 1 but not system 2.
04.) I would suggest you to try to find a clean basis for further analysis; means, update everything around on the system, especially Windows and the sound card driver (the real one, you wrote already FxSound is updated).
05.) Another thing, when everything is updated could be, doing a BIOS update for the affected system. But BEWARE! This is NOT WITHOUT RISK when you do not know what you are doing! Laptops/notebooks are somwhat custom and all-in-one system where manufacturers often fix general issues that way. You could start by searching your laptops manufacturers knowledge base for known issues in context of sound devices or ask their support.
What we are trying to accomplish is, sorting out as much possible causes as we can with general maintenance so far before going into more specific ones.
Next step, if you want to, try to see if the system “knows” of issues but did not tell you! Therefore, you can look at the categories “system” and “application” in the Windows Event VIewer. You can open it so:
https://www.isunshare.com/windows-10/6-ways-to-open-event-viewer-in-windows-10.html
Look for any errors (red-cross-symbol) which might be related to audio devices or FxSound directly. Maybe it does not start correctly at boot time which could fit your description and workaround.
I am afraid, for the time being, we are somehow digging in the dark a bit until we found a hint …