Without going too terribly much into those spoilers myself, I can say that the videos show off a lot of combat in various modes, including solo and party combat in both normal encounters, boss encounters, and an Eikon battle. The boss-level encounters showed off a number of quick-time events within battle, certainly more than I expected. Personally, I felt vibes of both Final Fantasy XIII and XV in the combat sequences.
There are some pieces that show where the devs are working towards that M-rating with the ESRB, as well; I caught a bit more bloody violence than we're used to in a Final Fantasy game during the Eikon battle, and I'm pretty sure I caught an f-bomb in one of the boss battles, though I admit I watched the videos at 1.5x speed due to a general lack of time this morning.
Gematsu also published a transcript of a roundtable with the executive team for Final Fantasy XVI, conducted earlier in February in conjunction with RPG Fan and Den of Geek. The interview touches a lot on bringing the "constant" elements of a Final Fantasy game into this new version that steps further into the action genre than any Final Fantasy before it. The entire interview is quite long and covers a number of other topics, too, including the design of boss and Eikon battles to mash-up genres and some questions about how the game looks pretty grimdark overall so far.
The media tour continues, too - Square Enix announced today that there will be another panel discussion about XVI at PAX East at the end of March (there will be a panel for XIV there, too). Final Fantasy XVI is still scheduled for a June 2023 release.
Source: Gematsu, Square Enix on Facebook