As @Cerberus says, it's an unusual but valid translation.
I think, however, it becomes clearer when one adds the beginning of the paragraph, so that it reads:
There is a saying much usurped of late, That Wisedome is acquired, not by reading of Books, but of Men. Consequently whereunto, those persons, that for the most part can give no other proof of being wise, take great delight to shew what they think they have read in men, by uncharitable censures of one another behind their backs. But there is another saying not of late understood, by which they might learn truly to read one another, if they would take the pains; and that is, Nosce Teipsum, Read Thy Self: which was not meant, as it is now used, to countenance, either the barbarous state of men in power, towards their inferiors; or to encourage men of low degree, to a sawcie behaviour towards their betters; But to teach us, that for the similitude of the thoughts, and Passions of one man, to the thoughts, and Passions of another, whosoever looketh into himselfe, and considereth what he doth, when he does Think, Opine, Reason, Hope, Feare, &c, and upon what grounds; he shall thereby read and know, what are the thoughts, and Passions of all other men, upon the like occasions.
In other words, he's contrasting reading oneself to reading books. People who read books may think themselves wise and put themselves forward as such, but to be truly wise one must read oneself. So I suspect that he chose "read" simply because the contrast between "reading books" and "knowing thyself" isn't nearly as striking as the contrast between "reading books" and "reading thyself."
That is to say, the choice of "read" as the translation was rhetorical.
What I find interesting is the claim that nosce te ipsum was used "to countenance, either the barbarous state of men in power, towards their inferiors; or to encourage men of low degree, to a sawcie behaviour towards their betters." I'm trying to figure out how that shift occurred and what the phrase meant in that usage.