I can help explain what the Byzantines meant by this, at least…a specialist in late antiquity might be better suited to explain what Manichaeism originally was.

Basically, it was a religion founded in Persia in the 3rd century by Mani, who taught that there was a spiritual world of light and a material world of darkness. It was popular throughout the Roman and Persian empires, and as far east as China, but it was persecuted by the Romans and then outlawed when the empire officially became Christian in 391. There were still Manichaeans in the Near East and maybe in parts of Europe after that, but it was persecuted as either a heretical kind of Christianity, or a kind of paganism.

If you follow the links on Wikipedia, the Manichaeism article notes that there is a figurative use, where even today anyone who has a dualist, “good vs. evil” outlook could be described as a Manichaean. Well, this is exactly the problem we have in Byzantine sources (and western Latin sources too). Sometimes, medieval authors use archaic terminology to refer to contemporary peoples. They wanted to show off their education and their knowledge of ancient literature and history, even if this often makes it harder for us to understand what they’re talking about.

Our source for the numbers of "Manichaeans" at Dyrrahachion is the Byzantine princess Anna Komnene, daughter of the emperor Alexios I Komnenos, who loves using archaic terminology. For example, she sometimes uses the term “Scythians” from classical history, for the Varangians, mercenaries from Scandinavia/Russia. So, when Anna or other Byzantine writers refer to Manichaeans, what they really mean are either Bogomils or Paulicians.

The Paulicians originated in eastern Anatolia/Armenia, perhaps influenced by remaining Gnostics or Manichaeans, or possibly by Islam. Paulicians were not exactly Manichaeans, but believed in a similar kind of dualism, where the material world was evil. That meant either that Christ incarnated into a fundamentally evil human body, or that Christ’s body was divine and incorruptible. This is how the Orthodox church saw it anyway; they rejected dualism entirely, and taught that Christ was fully human and fully divine.

The Byzantines regained control of eastern Anatolia in the 7th century, and while there was always a bit of effort to bring Paulicians (and anyone else they considered heretics) into line with Orthodox doctrine, sometimes they were tolerated or even favoured. In the 8th and 9th centuries there was an iconoclast movement in Byzantium, where some emperors and some members of the church were opposed to religious images of Christ or Mary or other saints. This actually fit in well with Paulicianism, since images were evil just like every other material things.

In the 10th century the Byzantines thought it would be better to resettle some Paulicians around Philippopolis (Plovdiv) in Thrace, where the Byzantines hoped they would be effective in fighting against the Bulgarians. They were, and Bulgaria was conquered in the 11th century. After that, the Paulicians sometimes rebelled or revolted against the empire, but sometimes they were also recruited into the army in exchange for money or land or titles. That’s what they were doing in Alexios’ army at Dyrrhachion in 1081. When Anna refers to "Manichaeans", she means Paulicians.

Perhaps not coincidentally, after the Paulicians settled in Thrace, a similar form of dualism appeared in Bulgaria and the Balkans, Bogomilism. The Bogomils were actually not quite dualists like the Paulicians, but believed that the devil had created the material world. The world was therefore evil, as was everything in it, including the church and its priests, and marriage and the other Christian sacraments.

Their beliefs may be more familiar as Catharism, which appeared in Italy and France in the 12th century and was probably influenced by (or even directly related to) Bogomilism. And of course, western Latin authors used archaic name sometimes too. Latin authors knew all about Manichaeism from the writings of Augustine of Hippo, who flirted with it way back in the 4th century before becoming a Christian. Then he frequently condemned it in his writings, which inspired much later authors to use the same terminology and language to refer to any heretics, such as the Cathars.

So, very short answer - the “Manichaeans” in 1081 were most likely Paulicians, and less likely Bogomils. The term could refer to anyone that the churches in Rome and Constantinople considered heretics.

Sources:

Peter Brown, The Rise of Western Christendom (Blackwell, 1996)

Samuel N.C. Lieu, Manichaeism in the Later Roman Empire and in Medieval China, 2nd. ed. (Mohr, 1992)

Walter L. Wakefield and Austin P. Evans, Heresies of the High Middle Ages (Columbia University Press, 1969)

John Haldon, Warfare, State, and Society in the Byzantine World, 565-1204 (Routledge, 1999)

Joan M. Hussey, The Orthodox Church in the Byzantine Empire (Oxford University Press, 1986)

John W. Birkenmeier, The Development of the Komnenian Army, 1081-1180 (Brill, 2002)

In sources on the battle of Dyrrhachium (1081), the term "Manichaean" was used generically in this case referring to the Bogomils, who were a Slavic dualist sect that originated in 10th century Bulgaria and was modeled on Manicheansm. Contemporary authors, both Slavonic and Greek, labelled them as "Manichaeans" in sources, which was used synonymously, and the Greeks called them pavlikiani (Παυλικιανοί) their existing word for the earlier Armenian Paulican sect that formed in the 7th century. The Byzantines had forcibly moved many of these Paulicans from Armenia to Thrace and their European frontiers in the centuries prior to scatter them and prevent a large concentration of them and to use them as border protection against the Bulgarians, so this Paulican population later inspired Bogomilism among the Bulgarians after their Empire was annexed when they became Roman citizens.

The Byzantines were tolerant of these groups to the extent that they demanded their military service when called upon in return for ignoring their "heretic" religious activities. So when the Roman army under Alexios I Komnenos heard of an imminent Norman landing along the Albanian coast/Strait of Otranto, he raised an army of Thracian, Armenian, and Macedonian tagmata and moved from Constantinople to Dyrrhachium, and along the way he recruited Balkan conscripts, Thessalians, and a few thousand of these Bogomils. The Bogomil population was concentrated in the south Balkans in modern-day North Macedonia and Bulgaria, and the recruited Bogomils were then organized into military units to fight in battle.

So I hope this answers your question.