I think the abstract game described by the article implies that one wouldn't directly see the change in the gender ratios, what one would see would a person who had become "desperate" and and began "underbidding". Once one person starts "underbidding", the effect can cascade as other feel pressure to match the "bids".

However, the big question is whether a dating site would be arena where that kind of dynamic would actually play out.

It's worth noting that in the present housing market, there's a also a mis-match between people looking to buy houses and available new houses. However, the banks and Real Estate dealers have managed hold back the flood-gates of desperate offers through various means - so market structure can put a damp on these ratio effects. I've evolutionary psychology theory that talks about the social pressure on women to not "sell themselves short" and this is another effort to control market structure to prevent the effects described in the article - but since Internet dating sites are a purely individual matter, they may be where ratio effects come into play.