Wireless Display Adaptor not detected by MacBook Air
As per Microsoft Wireless Display Adapter's Store Page:

Operating systems
Mac OS X
Mac OS 10.10  (Not Compatible)
Mac OS 10.9  (Not Compatible)
Mac OS 10.8  (Not Compatible)
Mac OS 10.7  (Not Compatible)

[In all likelihood, 10.11/10.12/10.13 and later are not compatible as well]
It will not work with a Mac.