I must have missed something. That page doesn't refer to women, children, or the elderly (or any group) that I can see. It also doesn't actually make the claim (though I'd say it's implied) that Aikido is effective for self-defense for those groups. It never uses a direct reference to fighting, though I think you and I would both read an implication of fighting in that wording.It’s claiming rather openly that it is an effective form of fighting that emphasizes method over strength, thus weaker individuals (women, children (LOL) and the elderly) can utilize its techniques to defend themselves against larger and stronger assailants.
Are the movements and principles of Aikido effective for self-defense? They've worked for me the few times I've used them (referring to the principles and movements I see as shared between Aikido and NGA), though they probably weren't necessary there. Others who use them more regularly (where being attacked and needing to control are part of their jobs) report more usefulness than I've had a need for.
I think we sometimes get lost in comparing to something else, which is actually arguing about "best". But "best for" isn't the same things as "good for", or even "can be used for". You won't find a lot of competition evidence (except within Tomiki), because Aikido isn't a good path for that - it takes too long and has too much focus on specific principles, rather than direct fighing effectiveness. Recognizing Aikido principles and movement in video also requires an understanding of those principles and movement, which makes it difficult to discuss with folks who don't have any experience related to it. Note that nobody looks at a jab in a video titled "MMA in a street fight" and says, "that's a jab - it comes from boxing". Sure it does. Also comes from other places, and is part of MMA.