I'm just going to call this game "Dodge-em" for the time being.
The goal of each level is to move your ship from the right side of the screen to the left, while successfully avoiding collisions with the obstacles placed randomly on the screen.
Your ship can't move right. It can only move Left, Up, and Down. It can go Left either fast or slowly. When moving Left slowly, you can move Up and Down faster.
The game also has a bonus which decreases continuously. The bonus will decrease faster if you're moving Left slowly. This bonus is awarded every time you pass a level.
If the area ahead of you in a straight line is clear, you can enter Hyperspace for the rest of the level. The bonus does not decrease when you're in Hyperspace. If the path isn't completely clear though, you'll ram into an obstacle and die.
The NES is known mainly for RPGs, platform games, and "Scrolling shooters". "Dodge-em" is none of these. That's why most NES fans probably won't like it.