I am trying to think of non-shooting / run&gun examples and Ecco the Dolphin’s famously trippy ending against ancient aliens has some distinct Giger vibes for the final few backgrounds and enemies. My apologies for the three decades old spoilers.
The Xenomorph also has a cute cameo in Outer Heaven in earlier versions of Snatcher (I believe up to the PC Engine version). The carefree pop culture references were replaced with Konami cameos in later outings, probably due to legal concerns.
The Gōma in Sakura Taisen wear their inspiration on their sleeves, so to speak.
Soon to reappear as cannon fodder in Super Robot Wars 30’s first DLC!
And, less about the Xenomorph specifically, there’s the obvious homage to the whole aesthetics of Alien’s first act in Streets of Rage 2’s third stage.