Real water and real wine are more complicates. More generally, after mixing some water and some ethanol the volume of the mix is smaller than the sum of the volumes. And this is not only a theoretical result, it's possible to measure the difference experimentally https://en.wikipedia.org/wiki/Alcohol_by_volume#Volume_chang...
You’re missing the point of the example by thinking of it as real. There’s no actual water or wine here.
Step 1: A with 10 L wine; B with 10 L water
Step 2: A with 9 L wine; B with 11 L liquid (10 L water and 1 L wine => 10/11 water, 1/11 wine)
Step 3: A with 10/11 * 1/11 = 10/11^2 L water; B with 1/11 * 10/11 = 10/11^2 L wine.
10 / 11*2 water in A ~ 10 / 11^2 wine in B.
The better way to understand it is to use only two cards, one face up one face down, if you give one to each person randomly, how can you magically match the other person? By flipping the card, because for every down you have, the other person has one up.
Most people won't consider the sub ml change in volume
https://chemistry.stackexchange.com/questions/111440/is-ther...
https://en.wikipedia.org/wiki/Alcohol_by_volume#Volume_chang...
Once you pour a liter of the new, mixed, wine-water substance back into the first container, you’ll likely have less than a liter in the second container, so the wine bottle will contain more than the container originally containing water. Right?