Edi, I find it extremely unlikely that Dom3 uses any Windows related RNG. The most obvious reason is that most of the time replays work exactly the same on different OSs.
IIRC (this is from a topic that was discussed a very very long time ago) the difference between OSs was due to an oversight, where there was a phrase similar to "if (random() > random())" and on some OSs the left random() was called first and on others the right random() was called first, which obviously completely alters how the battle plays out.
This may be the time to point out that the battles have some random seed associated with them and are played by using that random seed to simulate the battle. (The simulation remains identical through replays and OS changes because the random values are fixed since they rely on the random seed)
As an aside, depending on how Dominions generates random numbers, something extremely unlikely may be a bug (though considering Johan's response, I really doubt it). If Dominions uses a (huge) "table" of "pre-randomized" numbers (basically, a gigantic "sequence" of numbers that have been generated through some awesome RNG [like random.org's]) and asking for a random number merely fetches a number from the table according to some sequence (for example, the random seed for a battle may be a place in the table, and asking for a random number fetches the number in that place, asking for another random number fetches the number in the following place etc.), it is possible that the table does not contain a sequence of numbers that will allow something this improbable, in which case a bug may be involved.
And of course there's also vfb's debug analysis which might also point to a bug.
EDIT: ^- or maybe not, that remains to be seen. (Just see when mine and his posts were made
)