After seeing the direct, here are my thoughts.
1. Three Houses representing three different nations, monastery, officer's academy. So, your not just being called a teacher, you are the teacher! At an academy, where you teach students (units) to battle with. Go on...
2. You choose one of the three houses in the academy, and the students become your personal units to use in battle. Limited, but sure!
3. The girl from the last trailer (the one sleeping on a throne) is named Sothis, and has some kind of mind-link connection, thingy. Okay, but is she a manakete? I'm betting she is, because of the pointy ears.
4. There are fist weapons now?! YES!!!
5. So, you can earn money by having your students train with other students? Are there other methods of monetary gain?
6. Is there a Casual mode. I assume there is one.
7. The teacher's father is a mercenary named Jeralt. And they're another avatar character? (btw, female version's kinda cute though)
8. Leonie's... pretty cute! As are some of the other character designs (some, not all). It'll take a lot to replace Scarlet for me, though.
9. Promotions involve giving characters assignments? Guess that's to be expected; you are the teacher after all.
10. There seems to be a day/night cycle. Hopefully your given all the time you need for preparations.
Overall, I'm super hyped for this game! I can't to see more information about this in the future!