The glitch art seems like a good idea to me. I don't think it changes the "fairness" of using the original art one way or the other, but it could give your own project a more distinctive and cohesive look, particularly if you're using art from multiple sources. Making the image less static is a big plus in my opinion.
I don't entirely get what your UI will look like and how the glitches will play into the story, but I feel like there must be some way to spin the story for the visuals to make sense. Maybe your salvaged computer is having issues. Maybe the fluctuating power levels in the bunker mess with your screen. Maybe the apocalypse was something that specifically affected computer systems. Maybe you're watching your own stream so you can tell what viewers are seeing. Regardless, if there's one thing that video games have taught us, it's that players are usually willing to accept narrative dissonance if it's stylish/fun.