Thematically, Alien is cyberpunk. You have the megacorps, government take over by said megacorps, the orientalism, the techno-pessimism, the class divides, poverty, social decay, etc.

What's different is mainly aesthetics, which makes sense. It's in space, not a crowded city. Most of the settings are isolated and industrial, so they won't be lit up with neon and bright advertisements. The criminal/vagrant underclass that's ubiquitous in cyberpunk isn't going to be invited into these sensitive facilities, so even the janitors are more boujee than you'd expect to see on Earth.

We see ecological collapse, mass communication technology, and other traditional cyberpunk elements (including cybernetics, iirc) elsewhere in the extended universe, though not in the main films. The internet doesn't really work in space when signals take years to reach their destination, but an automated retinal display beaming propaganda directly into your eye, automatically flipping channels until it senses that you're sufficiently mesmerized by the newest cult sermons does appear in some of the old comics.