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Arx Libertatis (and Arx Fatalis 1.21) actually do have reverb, but the audio environment used (sfx/environment/alley.aef) is more subtle than the video you linked.

AF 1.21 and AL 1.0/1.1 might require EAX support in your sound driver for reverb with the DirectSound backend and the OpenAL backend in AL 1.0 and 1.1 does not support reverb at all. AL 1.2 (ie, dev snapshots) however always support reverb unless you replace the included OpenAL32.dll with an implementation without the EFX extension - all you need to do is enable "EAX" in the audio settings.

There is currently no way to change the audio environment through scripts or level files, but mods can replace alley.aef to change the environment globally to something with more reverb - the game data does include a couple of (unused) alternative .aef files. I have updated the .aef file format documentation on the wiki.

It's possible that the current implementation in AL 1.2 using OpenAL EFX does not exactly match AF 1.21 with EAX - comparisons would be welcome. In particular we currently use the AL_EFFECT_REVERB effect but from the name should maybe be using AL_EFFECT_EAXREVERB - I don't remember why we don't, possibly OpenAL Soft didn't implement it when I added that code. Otoh AL_EFFECT_EAXREVERB has a bunch of properties that the EAXLISTENERPROPERTIES struct used in AF 1.21 doesn't have so maybe AL_EFFECT_REVERB is correct.