Offering to email books or papers in the public domain or any that you have legal right to distribute (e.g. you are the author) is perfectly fine. This is not the case for the book in question. Please see this brief reference on US copyright.
Artin's Geometric Algebra was originally copyrighted in 1957 (registration number A00000271595) and was renewed in 1985 (registration number RE0000275074). As such, it will take until 2052 before distribution of this book without permission of Emil Artin's publishers or heirs will be legal here.
While the above refers only to US copyright law, the user who originally flagged the post mentioned that the same would apply in Germany (and I'm sure, in a few other countries as well). I will also note that while the legal policy of math.stackexchange does not obligate moderators to remove such an offer from the site, I can not in good conscience leave up any illegal material I am made aware of.
Copyright aside, offering to email a copy of a book adds no value to the site. Offering the name of the book and page number is fine, but summarizing the content and putting it here would be even better. We want the site to be as self-contained as possible. That's why I felt that my edit removed nothing of value.
I had reason to believe from this user's comments on the answer about his stance on copyright law and piracy that leaving a comment asking him to change his post would have no effect. Thus I edited the post myself, and when he attempted to revert it, locked it.
As for whether I made a mistake in not making a meta thread first, that's certainly possible. It simply never occurred to me that removing an offer to distribute an illegal copy of another mathematician's copyrighted work would be controversial enough (beyond 97832123 himself, whose attitudes towards copyright law and piracy were clearly given in the comments on that answer, then deleted by someone other than me) to warrant a meta topic. However, that meta topic has now been created. Further discussion of general policy towards copyright infringement should go there.