The Legend of Xanadu is a PC-Engine game - it’s just that, as far as we know, these tracks were composed first on PC-88/98 hardware before being arranged for PCE, because that was what Falcom’s sound team was used to at the time. The versions from the J.D.K. Special album aren’t used in the game itself at all, but they are the originals.
I did notice a lack of a mention of Falcom in the OP, so I’m here to rectify that with a brief(?) history of some of their work in the pre-Windows era - mostly on Japanese PCs like the PC-88 and 98, but also including some console games. I won’t be mentioning every single game or soundtrack, but I’ll go over many of them, and provide samples so you can follow the evolution of their sound.
While they were founded in 1981, it was in 1985 with Xanadu (composed by Toshiya Takahashi) on PC-88 that they really got their start musically - while its soundtrack was small, it was the genesis of a main theme that would continue to be used in several later games in the series. (If you’ve played Xanadu Next, you may recognize it.) Its 1986 expansion, Xanadu Scenario II: The Resurrection of Dragon, is especially notable for featuring the first work of the legendary Yuzo Koshiro, alongside Takahito Abe.
The Resurrection of Dragon (Koshiro)
Triumphal March (Abe)
The following year, in 1987, Falcom released Ys I, with Koshiro as the lead composer. He was joined by newcomer Mieko Ishikawa, with director Masaya Hashimoto contributing a single track as well. Falcom also released their very first arrangement album, All Over Xanadu, this year. The soundtrack release for Ys I would mark the beginning of Falcom’s relationship with arranger Ryo Yonemitsu, who would later provide arrangements for the PCE versions of Ys I to IV, as well as for various albums.
Fountain of Love (Ishikawa)
Tower of the Shadow of Death (Koshiro)
The Morning Grow (Koshiro)
To Altel (Abe)
Scenario II Ending Theme aka Triumphal March (Abe)
Beat of the Terror/Palace of Destruction (Koshiro, arranged by Yonemitsu)
Unfortunately, after this point, Falcom stopped officially crediting their composers by track, so all we’ve had to go on to figure out credits since then has been whatever information composers reveal in interviews, social media and the like, a few games that were released with telltale composer codes still remaining in the data, and our analysis of their styles based on this info.
Later that year, Falcom would also recruit Hideya Nagata and Reiko Takebayashi for Sorcerian:
The Lost King’s Scepter - Dungeon (Koshiro)
The Cursed Oasis - Sand Castle (Koshiro)
The Thieves’ Tower - The Seal (Takebayashi)
The Cursed Ship Queen Mary - Aboard Ship (probably Ishikawa)
The Mystery of the Red Jewel - Giant Moth (Nagata)
Medusa’s Head - Village (Koshiro)
Beautiful Day (Ishikawa)
Takebayashi would soon leave Falcom for Quintet (founded by Tomoyoshi Miyazaki and Masaya Hashimoto, the creators of the Ys series), but the others would stay around for Ys II in 1988:
To Make the End of Battle (Koshiro)
Ruins of Moondoria (Nagata)
Tender People (Ishikawa)
Subterranean Canal (Ishikawa)
Termination (arranged by Hiroyuki Namba)
Symphony Ys, released in 1988, is Falcom’s first orchestrated arrange album. 1988 would also mark the beginning of the Falcom Special Box series of albums. And perhaps most notably, both Koshiro and Nagata would leave Falcom not long after the release of Ys II, leaving Ishikawa as the sole composer for a year and a half. During this period, she would compose for Sorcerian Utility Disk and Additional Scenarios volumes 1-3 in 1988 and Star Trader and Ys III in 1989. As with Ys I and II, the soundtrack releases later on would contain a few arranged tracks.
(All of the following songs are Ishikawa)
Snow on the Gojo Ohashi Bridge
Castle Keep of Sorrow
Good Luck! Good Bye!
A Premonition =Styx=
Steeling the Will to Fight
Morning of Departure
Wanderers from Ys
Second Movement (Symphony Ys, 1988, Koshiro, arranged by Kentaro Haneda and performed by King Symphonic Orchestra)
Templo del Sol (Falcom Special Box '89, 1988, Abe, arranged by David Matthews)
The Seal (Falcom Special Box '89, 1988, Takebayashi, arranged by Takeshi Yano)
In the Memory (Falcom Special Box '89, 1988, Ishikawa, arranged by Hiroyuki Namba)
Snow on the Gojo Ohashi Bridge (Sengoku Sorcerian, 1989, Ishikawa, arranged by Hiroyuki Namba)
Ninja Mansion (Sengoku Sorcerian, 1989, Ishikawa, arranged by Hiroyuki Namba)
Mobile Satellite Mjölnir (Star Trader, 1989, Ishikawa, arranged by Keiichi Oku)
Star Trader (Star Trader, 1989, Ishikawa, arranged by Keiichi Oku)
Oath on a Starry Sky (based on Feena, Falcom Special Box '90, 1989, Koshiro, arranged by Keiichi Oku)
Protectors (Falcom Special Box '90, 1989, Koshiro, arranged by Anthem)