Hi! This is a fascinating discussion - thank you all for your insightful input! Maybe I can add some information (and hopefully not just confusion); I'm not an expert, but I have been doing some research in the past couple of days as I'm writing something about the Sound Blaster history. So I will take a look at most of the games that were mentioned here that may be the first titles using the Sound Blaster's PCM capability, and add a few myself.
For now I'll only look at games released along with or prior to the Sound Blaster card (November 1989), so all the 1990 titles - like Prince of Persia, Links, or Battletech - are out. Some of the information in this list is just what I gathered from this discussion.
A10 Tank Killer, M1 Tank Platoon: released in 1989, but as mentioned, those first release versions don't have Sound Blaster support.
Ghostbusters II: released in 1989, but - as you said - the dormant pre-release Sound Blaster support is broken, only being fixed in 1990.
Space Quest III: released in 3/1989 with dormant pre-release Sound Blaster support. However, Wikipedia says this (without sourcing it): "Though Space Quest III was designed to utilize the Sound Blaster's ability to play digital samples, the inclusion of an incorrect audio driver left the effects unavailable to IBM PC users with the Sound Blaster card." So it's the Ghostbusters II scenario again ...? Does anyone know more about this?
Other games using the OmniMusic sound driver on DOS: Most of those I could find were released after 1989, with two exceptions:
Take Down: released in 06/1989. Using DOSBox, I get nothing but PC speaker sound. Couldn't try real hardware though.
Ocean Ranger: released in 06/1989. Again, using DOSBox, I only get PC speaker sound.
Hole-in-One Miniature Golf (Deluxe): This is a tricky one. According to Mobygames, the original game - just called Hole-in-One Miniature Golf - was released in 1988 for the Amiga and other platforms, with a DOS port following in 1989. But this first DOS version doesn't include digitized sounds and Sound Blaster support, at least they're not mentioned on the box. Apparently those sounds were added with the DOS-only re-release called Hole-in-One Miniature Golf Deluxe, featuring additional courses and said digital sounds. Mobygames says it was released in 1989 like the original, but I find that unlikely, and the game files I found were created in 1992. A possible source for this confusion might be the labels of the 5.25" disks also shown on the Mobygames page for Deluxe, which say "1989" - however, those disks clearly belong to the regular, Non-Deluxe version of the game.
Tongue of the Fatman: released in 09/1989. Dormant SB support with a few digital voice samples, at least in the 5.25" version - the 3.5" disk version was released on just a single disk to lower the cost (presumably), but to make that fit, this version omits the samples.
The Manhole (CD version): This was the first CD ROM game for the PC, it uses digitized sound effects and music, and it was released in 1989. However, it doesn't seem to use the Sound Blaster PCM feature - just CD-DA tracks. I'd say that doesn't count as "real" Sound Blaster PCM/DAC support, but please correct me if I'm wrong.
EDIT: As Cloudschatze pointed out, there also was a floppy release of The Manhole, also released in 12/1989 (with the file being created in early September, even before the Fatman game). Even without CD-DA music, it uses some digitized music samples.
I would like to add another title to the discussion: In a recent Interview (see below), Creative's Sim Wong Hoo mentioned working with Brøderbund to develop the Killer Card, the prototype card which became Sound Blaster. Brøderbund, says Sim, was supposed to add voice output to their Carmen Sandiego learning games. According to him, those games were readily available when Sound Blaster shipped in 1989. Looking at the Carmen Sandiego series on Mobygames, only one (DOS) title seems to qualify: Where in Time is Carmen Sandiego? from 09/1989.
Mobygames shows several different versions of the box art and disk labels:
1) There was a DOS version with 5.25" disks and a copyright from 1989 on the box. However, it doesn't mention Sound Blaster - or any other sound card/technology - on the compatibility sticker on the cover. I found the files of a 1989 version which only gives me PC speaker sounds in DOSBox.
2) The box art for a 3.5" version of the game (as well as a dual-medium release with both disk types) looks the same again, including the 1989 date, but this time, the "compatibility" sticker lists some sound cards: AdLib, Tandy, Covox - and Sound Blaster. The disk labels say "1989/1990".
3) Finally, another 5.25" release featuring "version 1.2" of the game, according to the comments. It's the same box art again, including the 1989 date, and the compatibility sticker lists the sound cards as above. There's an additional "over 100,000 copies sold" sticker on the cover, indicating that this box was shipped quite some time after the original. The disk labels still give the 1989 date.
Watching some Let's Play videos on Youtube (including an LGR review), I couldn't hear any digitized voice samples - but the game does seem to use PCM sound effects. The videos I found don't mention the release date of the specific version they used, but looking at the title screen, it clearly says "copyright 1989/1991". The version used on LGR also shows the same box art as the "V1.2" above, including the "100,000 sales" sticker.
So ... I'm not sure, but it seems as if the original version didn't include digitized sounds, as those were added in an update at a later date for a re-release, either 1990 or 1991. Those Carmen Sandiego games got re-released a lot!
Looks like that weird Fatman game takes the crown - or did I miss something?
EDIT: As Cloudschatze said, The Manhole's disk version was made even earlier (but released later). So I'd say it's a tie 😀
The Wikipedia article about Space Quest III: https://en.wikipedia.org/wiki/Space_Quest_III
Minigolf Deluxe on Mobygames: https://www.mobygames.com/game/dos/hole-in-on … ure-golf-deluxe
The Sim interview: https://custompc.raspberrypi.org/articles/the … d-blaster-story
The LGR video: https://www.youtube.com/watch?v=5ln64lo9l5g
Carmen Sandiego on Mobygames: https://www.mobygames.com/game/where-in-time- … carmen-sandiego