Perhaps some kind of sample rate mismatch? Not sure how you'd fix it, though.

I might temporarily take out the SB16 from my 486 and see if it works correctly with that card on this system soon. I know it runs with no sound issues using that card on my 486, though obviously game performance is much worse.

I just tried it with an SB16 and the cutscenes work much better (they now stay in sync, too). The audio isn't absolutely perfect, there are some occasional small stutters and clicks but looking at videos of the game on YouTube I think they may just be how the game always is. It's a bit of a shame Delphine locked the audio to a lower sample rate on SB Pro compatible cards, too. I wonder if it would be possible to fix it on the ES1688, though.

Turns out that this may be a bug with the game's sound driver. I tried it in PCem and the exact same issue occurs on Sound Blaster 1.5 or Pro, but not SB16.

I'm sorry to necropost, but I felt like this info was important enough to warrant it. It is indeed possible to get this game to work properly on a Windows Sound System compatible card like the ESS I mentioned. I looked into this issue again and I realized this game uses Miles Design to handle the audio. For whatever reason this game does not include the digital sound driver for Windows Sound System, and I have no idea why because if you just copy the file SNDSYS.DIG from another game that uses Miles (in my example I used Theme Hospital) to the DATA\DRIVERS directory, Windows Sound System will now show up as an option for digital audio in the game's install program. You can then set that as your digital sound device and the game from what I've tried works perfectly, you get 16-bit audio and no more cutscene audio glitches. Insane they didn't just include it from the beginning.