Greetings - an interesting question ! I have been interested in the same issue since I saw footage from the game.
However I strongly believe it is necessary first and foremost to contextualize who these people were and where they came from. Cumans were a Turkic speaking tribal confederation of semi-nomadic pastoralists of the Ponto-Caspian steppes who were forced to migrate into the Kingdom of Hungary in the Carpathian basin during mid-thirteen century. The reason for their forced migration was the Mongol invasion- although it must be said that a lot of the West Eurasian Turks were also present within Mongols' ranks. Once in Kingdom of Hungary these semi-nomadic pagan people were gradually forced to settle down and accept Christianity. It was a long and excruciating process for all parties involved. Of course by the early 1400s the original kipcak-cuman confederation of western Eurasian steppes didn't exist anymore but was superseded by the Jochi Ulus (the Golden Horde) and its successor states.
Which brings us to Kingdom Come- that takes place in the kingdom of Bohemia - a western neighbor of Kingdom of Hungary- during the early fifteenth century and your questions.
Cumans as "godless pagans" was an often used invective - especially by Czech/Bohemian chroniclers and in letters of correspondence. During the times of war between the Hungarian and Bohemian kings Cuman contingents (in service of the former) were often send for brutal cheuvachee-like raids and Czechs were often on the receiving end of those - hence their disdain. For example a letter written by Czech king Přemysl Otakar II in 1260 and addressed to pope Alexander IV describes a vast polyglot army of Bela IV of Hungary whom Otokar fought at Kressenbrunn. In his army Bela had Hungarians, various Slavs, Tatars, Cumans and other "monstrous pagans". However by the 1400s most of the Cuman descendants in Hungary would be Christian. So the godless pagans appellation would be appropriate but to an earlier historical context.
This brings us to your second questions - the Turkic like military attire - which I interpret as the costume and gear of medieval Pontic steppe warriors. This is afaik a highly contentious issue further complicated by two interrelated phenomena. First - we have the observation by art history and archaeology that Cumans slowly adopted local material culture. Digs at Cuman burial sites show western straight double edged swords instead of sabres around 1300. The church frescoes of Saint Ladislaus cycle -in which the Cumans are a traditional element of the story- show them depicted in a more central European garb as one gets closer to 1400 (But still being depicted as horse-archers. Though this does not say much as the majority of Hungarian king's cavalrymen were horsearchers at that time anyways). Second phenomenon which makes a reconstruction of a Hungaro-Cuman warrior from around the time of Kingdom Come difficult is the fact that there is a gradually emerging influence of Turco-Levantine equipment (i.e. Ottoman Turks et al.) mediated via Byzanto-Balkan people. It is first noticeable only in some contexts and mainly in southern counties but by the battle of Mohacs in 1526 common Hungarian soldiers would be similar to Ottoman military personnel in garb and basic equipment.
Cheers !
Samuel
Tl;dr
The Turkic military attire: probably impossible to answer. But I would be highly skeptical. As the fifteenth century progressed there were definitely noticeable Turco-Balkan influences in both costume and equipment but this relates to all ethnic groups in Kingdom of Hungary and not only to (what remained of) Cumans. The face masks and lamellar armor I saw in promo material of the game is either anachronistic or not at all from Carpathian basin area.
The "Godless-pagan" - Not in early 1400s but throughout 1200s and perhaps into early fourteenth century they might have been viewed as such by Hungarian's western neighbors in the context of political propaganda.
For further study/ references I highly recommend to check the following:
https://ceu.academia.edu/KyraLyublyanovics - this scholar has several articles on Cumans and their integration into medieval Hungarian society.
Andras Paloczi-Horvath. Pechenegs, Cumans, Iasians: Steppe peoples in medieval Hungary. Hereditas, Corvina. 1989
B. Szabó János. A honfoglalóktól a huszárokig - A KÖZÉPKORI MAGYAR KÖNNYŰLOVASSÁGRÓL. ARGUMENTUM. 2010
Kovács S. Tibor. Huszárfegyverek a 15-17. században. Martin Opitz kiadó: 2010
Nóra Berend, “Cuman Integration in Medieval Hungary,” in Nomads in the Sedentary World, ed. A. Khazanov and A. Wink (Richmonds, Surrey: Curzon Press, 2001)pp. 103 -127
You might also check the all the works of Russ Mitchell - he is one of the few Anglo-American scholars who deals with the military side of Cumans in kingdom of Hungary. For example one of his article goes in depth on Cuman's military equipment.
Russell Mitchell, "Light Cavalry, Heavy Cavalry, Horse Archers, Oh My! What Abstract Definitions Don’t Tell Us About 1205 Adrianople ," in Journal of Medieval Military History: Volume VI. pp. 95-118