It's Galaga with procedurally generated scripted events. You go into a menu whenever one of these events occurs, and it rolls a dice (just so you know we're on theme!).
In most games, they wouldn't interrupt the gameplay to do the procedural events. They would just run the calculation in the background, and then you would get whatever event you get, which is the better design choice. However, in an attempt to superficially fit in with the theme, this game exposes the procedural event generation as a "feature," and the gameplay experience is interrupted.
If you're going to do procedurally scripted events, just take out the dice rolling screen altogether. It doesn't add anything.
The name "Endless Space" is probably a trademark owned by Sega, the company that owns the Endless Legend franchise, which has a 4x title called "Endless Space." I'm no lawyer, but this might be trademark infringement.
The guns shoot too slowly and the action is generally too slowly paced for a Galaga-like. Galaga is fun because you move quickly and shoot quickly. Compared to Galaga, this feels like molasses.