Hope I didn't give too much away, should you still want to watch it at some point..
Since I do plan on watching the sequels someday, I mostly skimmed over your post, Rijst.
Since you said it'd take an 8-bit version I thought it was ok to drop some spoilers..

I saw the first Matrix movie when it first came out and I thought it was great. But I hated the impact it had on the film industry. Action films were never the same post-Matrix and that bummed me out. Plus, I was annoyed by how ubiquitous The Matrix quickly became. Everywhere you looked, black trench coats, wraparound sunglasses, and people with that, uh, "raining binary" screensaver. By the time the sequels came out, I was sick of the whole Matrix thing.
Also, Neo seemed like an invincible god at the end of the original, so there didn't seem to be much of a point in making sequels. It seemed like they'd be as dull as trying to beat a game with an invincibility code on.
It was definitely "hot" at the time. I haven't seen the films in a few years to be honest, it probably comes across as dated by now. The moves Neo makes in this clip after he jumps onto the balcony are just plain silly.
Watching that made me realize that the choreography of the fighting is so much more interesting in The Matrix than it was in the Star Wars prequels. They're both too clean in my opinion.. could use a bit of grit and emotion.. but The Matrix does it a lot better.
Which movies do you think portray this well? Most fights in Game of Thrones are quite dirty and do this really well in my opinion. A bit exaggerated on the splattering maybe..
Grit is the new word in entertainment these days I think. It seems there are very few all-out good or bad guys anymore. Heroes are often also criminals, drug addicts or both, living in the "real world" and often having some sort of fatal flaw. A bit like in ancient Greek tragedies really. Maybe that's just the limited selection of stuff I watch though, not having a tv etc..