I searched through Wikipedia about instances of Greek fire being used from armies other than the Byzantines and it offers no examples of its use by anyone else other than the Byzantines in naval engagements. At most, some Byzantine ships were captured by hostile powers:
...the Byzantines could not avoid capture of their precious secret weapon: the Arabs captured at least one fireship intact in 827, and the Bulgars captured several siphōns and much of the substance itself in 812/814. This, however, was apparently not enough to allow their enemies to copy it. The Arabs, for instance, employed a variety of incendiary substances similar to the Byzantine weapon, but they were never able to copy the Byzantine method of deployment by siphōn, and used catapults and grenades instead.
Additionally I searched about fire ships which I gather historically were used more as the again in-game demolition ships, and exploded on contact with enemy ships rather than use flamethrowers.
Then my search on thermal weapons was more interesting as it states that:
Similar petroleum and bitumen-based incendiary mixtures had been known for centuries before the invention of Greek fire, but this new recipe created a blaze which was extremely difficult to extinguish. It burned on water, and was used effectively in naval warfare, although it was primarily an anti-personnel weapon rather than a ship-burner. It remained effective at sea even after its use had declined on land after the 13th century. The Greek fire recipes continued to be developed over the centuries, and by the High Middle Ages was much more sophisticated than the early versions.
Duarte Barbosa ca. 1514 listed weapons made by Javanese people, including Greek fire. Zhang Xie in Dong Xi Yang Kao (1618) mentioned that city of Palembang, which has been conquered by Javanese, produces the furious fiery oil (ming huo yu), which according to the Hua I Kao is a kind of tree secretion (shu chin), and is also called mud oil (ni yu).
It much resemble camphor, and can corrode human flesh. When ignited and thrown on water, its light and flame become all the more intense. The barbarians use it as a fire-weapon and produce great conflagrations in which sails, bulwarks, upperworks and oars all catch fire and cannot withstand it. Fishes and tortoises coming in contact with it cannot escape from being scorched.
As such, this seems to indicate that some form of flamethrowing weapon was in naval use in the east although the delivery system somewhat differs from the one depicted in the game. The above extracts do not confirm, as I understand it, the use of naval weaponry, similar to the Greek fire, by Western European powers.
From the game's wiki the following claim is made:
Other civilizations acquired the secret of Greek fire at times, but it was so closely guarded and dangerous to use that it is lost today.
Therefore, what I whould like to ask is, if there are documented cases of Greek-fire, wildfire, or any relevant weaponry with a delivery system similar to that of a Byzantine dromon in Western European naval warfare.