This article misses some very important points. If this article is representative of Green’s book, I would be disappointed in him. (I suspect the reporter is getting a lot wrong here.)
It’s widely accepted by linguists that women are more likely to be language innovators than men. This isn’t surprising in the least for those that seriously study language. If there has been a lack of female-created slang in dictionaries, it’s most likely because traditionally men have controlled the publishing industry, and the slang that gets recorded is male-oriented or male-mediated. The phenomenon of female slang is nothing new, just more visible nowadays that women are in control of their own publishing outlets.
That a particular slang should develop among a particular internet group is also not surprising. Virtually every internet group has its own in-slang. Mumsnet is interesting in its own right, but there are no new insights into slang in general here.
And several of the terms they discuss, such as OTOH and FWIW, are hardly unique to Mumsnet. They’re in general use.
Also, sapphism refers to lesbians, not women in general. I don’t think a parenting website would have much lesbian slang. (Not that lesbians aren’t parents too, just that the topics of discussion on a parenting website are unlikely to be queer-oriented.)