Does the ASUS XG27AQDMGZ R 27-inch QHD OLED run 240Hz over HDMI 2.1, and what video ports does it include?

No, the HDMI ports are HDMI 2.0, and only support up to 144hz at the native resolution of 1440p; there is 1 DisplayPort 1.4 and 2 HDMI 2.0.

What's the difference between the XG27AQDMGZ and the non-Z version of this monitor and why is this one cheaper?

The Z is a best buy model and the non Z is the regular model. Main difference is the z doesn't have aspect control

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ASUS ROG Strix 27 inch QHD 2K 1440P 240Hz with AMD FreeSync Premium & G-Sync Compatible 0.03ms Glossy OLED Gaming Computer Monitor XG27AQDMGZ

27" QHD (2560 x 1440) glossy WOLED gaming monitor with 240 Hz refresh rate and 0.03 ms response time for immersive gaming
Highly efficient custom heatsink, advanced airflow design, and ASUS OLED Care functions to reduce the risk of burn-in
ROG-exclusive OLED Anti-flicker technology helps reduce the flicker during refersh-rate fluctuations
Third-generation WOLED technology provides brighter full white windows, clearer text, and improved motion clarity
Optional uniform brightness setting ensures consistent luminance levels
DisplayWidget Center software allows users to easily access OLED Care functions and adjust monitor settings using a mouse
Qualifies for 3 months of the Adobe Creative Cloud All Apps plan, purchase must have been made between September 15, 2021, and August 31, 2026