will this cooler fit this case?

It isn't as simple as that.

The case is 200mm wide but you have to allow for the thickness of the side panels, the space taken up by the motherboard tray and and space behind it, the standoffs, the height of the CPU socket on the motherboard and anything else I haven't thought of.

However:

Our built-up Mugen, despite a height of 16 cm is still room for improvement. According to the manufacturer cooler can fit up to a height of 16.5 cm in the Asgard Pro.

Review

You might struggle to fit fans to the side panel though, certainly one at the top.
 
I wouldn't put side panel fans on anyway, they're usually an annoyance in messing up good case airflow. That cooler should fit fine, hardly the biggest cooler out there! :)
 
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