So why thai goverment website claims otherwise (linked upper)?
I understand you are very educated about visas. But lets be clear here. Establishing and running business is not thing that most of expats/ed-visa tourists tend to do, as it comes with costs and responsibilities. So you won't find a lot of discussion of these visas here.
You get the extension for being thai business owner, not director.
Term director seems to be a bit confusing term here for some. You can hire some bar girl for being director 50baht an hour and still you own the company.
You are also trying route this conversation totally different way, which does not contribute the conversation nor help OP. What i'm trying to say is even if OP is not in the companys payroll anymore, he still be eligible to keep is business visa.