Does this cable support high refresh rates for gaming?

Yes, the cable supports high refresh rates including 4K at 120Hz and 1440p at 240Hz due to its UHBR10 capability.

What is the maximum resolution supported by the StarTech 3ft DisplayPort 2.1 Cable?

The maximum resolution supported by the StarTech 3ft DisplayPort 2.1 Cable is up to 8K at 60Hz using a compatible DP source and display.

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StarTech 3ft DisplayPort 2.1 Cable VESA Certified DP40 DisplayPort Cable w/UHBR10/HDR/DSC 1.2a/HDCP 2.2 8K 60Hz DP 2.1 Cord

Resolutions up to 8K 60Hz w/DSC, using a compatible DP source and display
UHBR10 supports high refresh rates including 4K 120Hz and 1440p 240Hz
High-Bandwidth Digital Content Protection (HDCP) 2.2 for a secure connection between source and display
High Dynamic Range 10 (HDR10) for higher contrast ratio and vibrant picture quality
Display Stream Compression (DSC) 1.2a for maximum resolution output
Multi-Stream Transport (MST) for daisy-chaining multiple monitors
32 Uncompressed Digital Audio Channels
Backward compatible with previous DP versions