Really expected you to weigh in on this.

Apologies ... sometimes life interferes ... been a very busy few days 😞 

It appears there is an issue with ffmpeg/ffprobe that is installed on your system.

The static version comes with its own ffmpeg and ffprobe - the shared version uses the ffmpeg/ffprobe version that comes with your system.
The shared version is only there as it is a much smaller distribution, which some prefer (and why wouldn't they if they already have ffmpeg/ffprobe on their system). Not being the most experienced user, half the time I do not know what to expect from the wild and crazy variation of distributions.

As for the location, an experienced Linux user once suggested using "/usr/share/RenameMyTVSeries" (see also the readme.txt), but I always have it somewhere in my home directory (~). Installing in "/" is a bad idea indeed - on any Linux distro. I have no clue what the recommended location would be usable for all Linux distros, well except for a location somewhere in the home directory (me not being an expert). Not sure if "/usr/share/RenameMyTVSeries" is bad under Arch or not.

I think it might be the way you have it linked cause the one thing I didn't do during my test was actually hit rename, cause the files I tested with had already been named properly. The tests were just to see if the drag-and-drop would finally work properly. I say the above cause under Metadata Option the first option says "[DISABLED - ffprobe is missing] Enable FFprobe". Grabbed a new series and none of the files will rename. Tells me renaming failed.

As for ffmpeg working correctly or not it's fine cause I'm able to use both MKVToolNix and Handbrake without issue. I just did a permissions check and other than having a few extra permissions they match what you have in the readme.

-rwxr-xr-x 1 cccp64 cccp64  362696 Jul  2 12:02 ffmpeg
-rwxr-xr-x 1 cccp64 cccp64  206312 Jul  2 12:02 ffprobe
drwxr-xr-x 1 cccp64 cccp64     120 Oct  3 08:24 icons
-rwxr-xr-x 1 cccp64 cccp64    2646 Jun 11  2020 readme.txt
-rwxr-xr-x 1 cccp64 cccp64 5605336 Sep 28 02:44 RenameMyTVSeries
-rwxr-xr-x 1 cccp64 cccp64     375 Jun 11  2020 RenameMyTVSeries.desktop

FAILED: /mnt/My Files/Television/Last Night's/Hacks (2021))/Hacks Season 1/Hacks.S01E01.There.Is.No.Line.EAC3.5.1.1080p.Bluray.x265-iVy.mkv -> /mnt/My Files/Television/Last Night's/Hacks (2021) S01E01 There Is No Line.mkv (ERROR: ffMPEG failed to create new file)
SKIPPED: /mnt/My Files/Television/Last Night's/Hacks (2021))/Hacks Season 1/Hacks.S01E01.There.Is.No.Line.EAC3.5.1.1080p.Bluray.x265-iVy.mkv -> /mnt/My Files/Television/Last Night's/Hacks (2021) S01E01 There Is No Line.mkv (File not renamed - Renaming original mediafile failed.)
FAILED: /mnt/My Files/Television/Last Night's/Hacks (2021))/Hacks Season 1/Hacks.S01E02.Primm.EAC3.5.1.1080p.Bluray.x265-iVy.mkv -> /mnt/My Files/Television/Last Night's/Hacks (2021) S01E02 Primm.mkv (ERROR: ffMPEG failed to create new file)
SKIPPED: /mnt/My Files/Television/Last Night's/Hacks (2021))/Hacks Season 1/Hacks.S01E02.Primm.EAC3.5.1.1080p.Bluray.x265-iVy.mkv -> /mnt/My Files/Television/Last Night's/Hacks (2021) S01E02 Primm.mkv (File not renamed - Renaming original mediafile failed.)
FAILED: /mnt/My Files/Television/Last Night's/Hacks (2021))/Hacks Season 1/Hacks.S01E03.A.Gig's.A.Gig.EAC3.5.1.1080p.Bluray.x265-iVy.mkv -> /mnt/My Files/Television/Last Night's/Hacks (2021) S01E03 A Gig’s A Gig.mkv (ERROR: ffMPEG failed to create new file)
SKIPPED: /mnt/My Files/Television/Last Night's/Hacks (2021))/Hacks Season 1/Hacks.S01E03.A.Gig's.A.Gig.EAC3.5.1.1080p.Bluray.x265-iVy.mkv -> /mnt/My Files/Television/Last Night's/Hacks (2021) S01E03 A Gig’s A Gig.mkv (File not renamed - Renaming original mediafile failed.)
FAILED: /mnt/My Files/Television/Last Night's/Hacks (2021))/Hacks Season 1/Hacks.S01E04.D'jewelry.EAC3.5.1.1080p.Bluray.x265-iVy.mkv -> /mnt/My Files/Television/Last Night's/Hacks (2021) S01E04 D’Jewelry.mkv (ERROR: ffMPEG failed to create new file)
...

Seems I made a mistake uploading GTK Static for 2.3.12 - uploaded the correct one now. Please try that one.
(included the shared ffmpeg/ffprobe instead of the static ones by accident)

Note: this may not be related to the issue you're running into.

@hans OK it's working, not perfectly but working so I personally can live with it. Thanks

I dragged 3 files to it, correct names found in under a second, on clicking rename did so without issue. tried a couple of other files and took about 3 minutes to grab the right noame, but on clicking on rename did so without issue. Like I said I can happily live with it.