I like this animation - if I'd seen it before I'd have used it in teaching. But inevitably it has rather simplified things: please forgive me if I get geeky biological at this point.
The reshuffling of genetic material between chromosomes in the process of meiosis occurs because, as the animation shows, parts of matching (homologous) chromosomes are exchanged. These crossover points are called chiasmata; there are likely to be a handful of chiasmata between larger chromosomes and one or two between smaller chromosomes. Now even the shortest chromosome is about 51 million base pairs long, so the deduction is that the reshuffling is of large chunks rather than small sections, even over several generations, and that specific DNA sequences will be conserved. The very large size of the genome and the small number of chiasmata makes the card-shuffling analogy quite limited (would be a great teaching/discussion point!); perhaps it's better viewed as the small child shuffling cards, where he merely swaps three large handfuls of cards rather than shuffling individual cards. That's why DNA testing for STRs - short tandem repeats - can work as the repeated sequence is inherited as a block unless it's very unlucky and ends up with a chiasma.
