It's not the original Elite as you might experience on other 8 bit era platforms. But instead puts the player into scenarios to beat. Also for me too, was something I never experienced back in the day, so was something of a joy to catch up with many years later. Enjoy!
IIRC that's just the opening training scenarios (what we'd now call a tutorial), though I might be misremembering.
On a side note, what's most impressive about the Nintendo version is the NES had a completely tile-based graphics system. It could only display sprites and flat blocks of background textures. This was part of what allowed it to do smooth scrolling in 2D platformers, which was something more powerful PC hardware struggled with for another decade, but with the trade-off that it couldn't just draw arbitrary lines on your screen, everything had to come from a raster image held on the cartridge.
Yet, they managed to get 3D wireframe working on the system. And more smoothly than some other computers without these limitations. In the background, the NES is having to calculate the wireframe outlines of the spaceships and stations and asteroids, break these into blocks, and bake their outlines down to raster image squares, which it then writes to a special memory chip on the cartridge, which the system then reads as a sprite.
So the game is making its own sprites/tiles up as it goes along. And doing that for every single frame.
I'm not a programmer or anything, so maybe it isn't really a big deal, but I've always been impressed that they could get the Nintendo to do that.