Yes, the Elgato Game Capture 4K S is compatible with the Xbox Series X.
4K S's own comparison table recommends it for Xbox Series S, not Series X -- Series X is only in the 4K X row. The card still passes video (HDMI auto-negotiates to a supported resolution), it just can't reach the frame rates Series X is capable of outputting.
Limitation
Elgato does not officially recommend 4K S for Xbox Series X -- only for the lower-output Xbox Series S. 4K S's HDMI input is version 2.0, which maxes out passthrough/capture at 2160p60. Xbox Series X's HDMI 2.1 output supports up to 8K HDR and 4K at higher frame rates; connected to 4K S, the console will auto-negotiate down to a mode the card supports (up to 2160p60), losing access to Series X's higher frame rate modes rather than failing outright.
“Recommended for Switch 2, PlayStation 5, Xbox Series S, Mobile devices Switch 2, PlayStation 5, PlayStation 5 Pro, Xbox Series X, PC”
Last verified:
Confidence: high confidence