Full disclosure: I don't have a Mac and I've never set up an active shutter 3D display of any sort. I will NOT be able to tell you anything for absolutely certain. But with no one else responding to you at this time I'll tell you what I do know!
Unfortunately, I think your suspicion about whether the laptop's display is compatible is the real problem. The related post you referenced seems to be mostly talking about getting 3D to work with unspecified monitors, so I get the impression they are using other monitors (not the laptop's display). According to this related post which references this article your monitor needs a refresh rate of at least 120Hz. I was not able to find anything conclusive about a MacBook Air's screen's refresh rate (I'd need to know which model/year of the MacBook Air you have for one thing) but I would be surprised if it did support anything over 60Hz. Laptop screen's are not likely to support high refresh rates in my experience (again, I don't know, and you should look up your model and make sure).
But even if it does support 120Hz, it's just not that simple. Typically for monitors to support 3D properly they need to be designed "3D ready" for it to be likely to work reliably. Even if your monitor seems like it has all the specs for it, so much has to go exactly right for the active shutter glasses to sync up with the monitor and produce a consistent 3D effect that unless the monitor was designed for it, it just probably will not work. (Again, you should look up your model and see if it mentions a "3D ready" monitor or "stereo compatible" or anything else indicative like that anywhere.)
Add on top of that any complications with actually setting up Blender to cooperate with the active shutter 3D on Mac OS, and I think your chances of getting it to work are not good. Also, you would definitely have to find a pair of active shutter 3D glasses with Mac OS compatible software, which could be tricky.
But as I've been stressing throughout this whole post: I don't know. I'm not an expert and I don't know enough about your machine. It just seems unlikely.
Sorry for all the disparaging news, and sorry for not being very authoritative! Good luck.