This is far better than either of the sample emails in the article, but I would cut out the second stanza - communication to managers about management shouldn't really be global.
Why shouldn't communication to managers be global? In this case it is an important part of managing expectations, which is part of culture.
With it in, people have a pretty good sense of whether they are likely to be impacted. With it out, people will assume that they are impacted whether they are or not, and will resent it. Also including it in what everyone got significantly reduces the risk that some low-level manager who never liked the work from home policy will try to eliminate it locally.
Those strike me as pretty good reasons to leave it in.
