So, just to play devils advocate for a second. There are several complicated issues here that are not as cut and dry as people would want to make them.
The first, is the idea of a female only competition. So the first question you have to ask yourself is, do you think that female only competitions are good, bad, or maybe just ok?
The standard justification for such an event is that, for many competitive events, without enforced sex (biological sex) regulations, female competitors do not have a realistic chance of out performing their male counterparts. This is simply a realistic evaluation of standard physical body plans, biologically female humans simply have different proportions and muscle load outs than males, on average. So, with no female only events, it would be functionally impossible for female athletes to win/place in almost every athletic event that female athletes currently participate in. Given this, it is common for people to host female only events, and generally speaking I agree with the practice as a sort of necessary evil.
However! These events and competitions divided by sex nominally are events where only the physical biological distinctions between male and female are taken into account. For example a GO tournament should be unisex, to host female/male GO tournaments is to assume that biologically female humans are functionally worse at a purely mental task. This is a VERY controversial assumption, and one that would be largely refuted by most research I have ever seen regarding the impact of sex on intelligence.
So, is league of legends an event where the physical differences between male and female justify a division of competition? In my honest opinion, no, league of legends is not such a competition. I would imagine the main difference that is seen in the volume of skilled league players by sex could be explained by cultural imperatives rather than biological ones.
So, Garena's made a miss step here I think, but given the existence and acceptance of female only competitive events, and an understanding of the comparative populations of skilled players by sex, it is not a 'OMFG CRAZY MISOGYNISTIC BASTARDS' kind of mistake, it is more of an an expected one. (still wrong though)
However, assuming you want to host a competition for female competitors, you do suddenly have a very serious issue to think about. What do we consider "female" and what method do we use to determine who is "female". Obviously this confusion comes from the fact that Female exists both as a Gender, and as a Sex.
For example, if I am biologically male, but gender identify as Female, can I compete in a womens tennis tournament? NO I can not. Well, that one is pretty easy, it assumes we define "female" biologically, but is it fair to assume everyone (Garena) sees it that way. What about someone who is Biologically Female, but Gender identifies as Male, if you think Gender is the more important definer of "female" then the second person can't compete but the first person can. And what it seems like in the case of Garena, if you think BOTH are necessary (biologically female who is also gendered female) Then you would nee a rule, something like the one they laid out, to insure fair play in your competition and preventing "Male" players from sneaking in.
In summation, Garena's position is that the nature of league of legends justifies a "female" only competition, and they define "female" as being biological and gender based. As a result, you get the thing they just posted.
While it is easy to see how people could disagree with BOTH of Garena's assumptions here, (personally I do) It is hard for me to see the OUTRAGE that people seem to be feeling. These are both boarder cases on issues that exist in a very wide facet of competitive events and Garena is hardly taking a radical or totally uninformed view of these issues.
Of course I posted this ten hours after the fact so nobody will ever read it.