From looking at coding, Area, Species and Gender do determine the game(although they could change the relationships anytime). Back when the JP Dream World came out I worked on this same chart, but I only ended up covering the original Forest Pokemon. It's on my blog if you want to combine the two lists -- I also came up with that Lotad was the only (0pt) Forest Pokémon which chose its game by Gender, didn't realise there were many more discrepancies in the Sky. I should have a look at it again, as by examining the coding I should get something like 70 data points a day... Female data is still rarer though.My original idea here was that there was a direct correlation between score and the moves a Pokémon has... so above a certain threshold you would always get extra moves. That seems to have been disproved today, as I played Ice Cream Scoop and got a Bidoof with Aqua Tail, then played it again, got a much higher score, but got a Sentret with no additional moves at all. If it is, as you say, a probability thing, then that's much harder to measure...
I am now pretty certain that both a Pokémon's species and gender determine the game it chooses. I haven't yet come across a situation where a Pokémon of a given species and gender will ask for different games... well, with the exception of Hoppip, whose can be found both in the forest and in the sky. Hoppip's extra moves also differ depending on where it is found, so it seems like the DW treats Forest Hoppip and Sky Hoppip as separate entities.
I also found one circumstance where both males and females of a species will ask for the same game: Zubat. This doesn't violate my hypothesis that gender predetermines what game is chosen, since both genders may be set to the same game, but it does make it potentially less useful for determining gender before playing. There may be many more females who choose the same game as males, but the rarity of females in the DW makes this hard to determine.
In any case, these are the preferences I've observed over the last few days: