As usual, the answer slides in at the confusing crossing point of: "yes, but... well no, but kinda..." territory that's so fun.

So what we are looking at are basically morion helmets. A type of helmet so very famously Spanish in style from the 1500s that regardless of where one is made it tends to be regarded as "Spanish". Now, of course, all things Spanish was fashionable at the time, so other people and nations copied the style. They were not a uniquely Spanish style. The Pope's Swiss guard use them in their historical dress uniform to this day. Unsurprisingly the Swiss guard were founded in 1506 and used the most fashionable style of their day being in the pay of the most illustrious of paymasters. If you wanted to anchor your look in the 1500s and as immediately recognized as Spanish a morion helmet is the way to go. So far so good.

Now, morions were more of a helmet for arquebusers or crossbowmen as it doesn't restrict vision as much, and a properly armoured swordsman would likely have worn a burgonet. The guys in the videos do not strike me as "ranged troops" what with all the armour and sword fighting they do. That said morions were popular throughout and morions and very similar helmets are popular amongst all sorts of infantry.

Properly armoured, though, that is not what conqistadors were, or at least ended up being. There was a lot of usage of indigenous (or inspired by) armours as "proper" European armour was heavy, hot and above all rusted away in the tropics (even though effort was made to avoid just such a thing by e.g. blackening or blueing armours). So the long campaigns with basically no proper resupply would end up with rather ragged soldiers and much lighter armoured as it was not only better considering the environment, but also the better choice in many ways. The conquistadors were a long way from home and being an adventurous lot didn't mind stealing a good idea, even from Indians.

So, "tricked out", well that's a bit tricky. Morion helmets could be very fanciful in style, high brims and ridge, and heavily decorated. I even have some nice pics from examples in the Met in NYC. However, these are generally ceremonial or parade pieces and thus not exactly typical, which kinda is why they are at the Met as art objects. They'd be expensive and stuff like gold inlays and filigrees and such meant less protection as you can't harden the steel properly. Most importantly the conquistadors were simple folk for the main part, the reason they went to the New World was precisely not being able to afford such grandiose and lavish pieces of armour but thought they should! Or at least be able to realise that ambition of becoming a noble more than just on paper.

The most egregious thing there are the face masks. I don't know where they are getting that. That wasn't a normal thing in European armours, certainly not with a morion which is worn precisely so it doesn't cover up your face. The only thing even close to it comes from a parade armour gifted if my memory doesn't fail me from the Holy Roman Emperor to the king of England, but I'll be darned if I can find it to check the details right now. It looks somewhat grotesque compared to the slick things in the clips, that remind me more of things Samurai might wear, and belonged to full knights suit with an enclosed helmet shaped to look like a head complete with a face with horns and glasses. I always think I'd be insulted by getting an armour like that, it really looks like a pointdexter caricature, just you know rendered in full plate.

Personally, I suspect the game developers are trying to avoid the hassle of animating faces and then having players call them on the uncanny valley effect all the time. And jesus the fantasy shoulder plates, why always the shoulder plates?

TL:DR, decorated morion helmets do exist, just not with facemasks to the best of my knowledge. They would not have been run of the mill, in reality more for ceremonial/parade work and conquistadors would be unlikely to use them precisely because they'd be expensive. They'd be using a more "munition" grade armour as these were practical people involved in a dirtybusiness where practicality more than style would decide their day to day actions.

For a broad discussion of arms and armor used by the Conquistadors, I'd recommend this earlier post answered by u/400-Rabbits and u/Yawarpoma. Their discussion of equipment constraints imposed by the environment versus the desire to conform to a certain identity by wearing European style armor is especially worthwhile.

The type of helmet depicted in the trailer appears to be a "morion", a style which may possibly have been around during the early 16th century, and certainly came in highly decorated versions, but was really only widespread in the second half of the 16th century. The Conquistadors, perhaps depending on their own class and wealth, more likely wore something resembling either a kettle hat/capacete or a sallet. Interesting note, the image of Atahualpa's execution in Guaman Poma de Ayala's New Chronicle appears to show Pizarro's men wearing helmets with hinged visors, very different from the trailer.