There are a few things I'd like to mention though.
The campaign map thing looks and feels an awful lot like Starsector. Mentioning this because... Well, you all know the game :p. I think I might change that, but I don't know what could possibly work better. The touch controls work fairly well with it.
Also, something I didn't mention in the video, the formation of the ships you see in the world map fleet matters. There are three "columns" of ships, one for each button. The first in each column is deployed automatically at the start of the fight, while the rest of the ships need to wait a set time (same time as it takes to move the ship), and you must deploy or retreat the ships in order. You'll be able to arrange the ships as you please.
The reason for this is primarily to make deployment smoother. Rather than bringing up a large menu of your ships, you only have 3 to choose from based on your formation, reducing clutter as well as making it a tactical decision.
Currently only 5 ships may be deployed on either side, at any given time. This will probably be more or less depending on how much larger a fleet is compared to the other, with the lowest being 3, and the highest being 7. Still no more than 10 ships at a time.