Your question starts off with a wrong premise. The alignment of the biscuit joiner in the slots made at 2:04 is quite precise. At 1:20 to 1:28 he makes 3 pencil marks across the join line of the two pieces. He sets one aside and makes slots, using the pencil marks to align the BSCM. When done, he takes the first piece and rotates it 180 degrees so that he is looking at the corresponding pencil marks on the second piece, then aligns the BSCM to those marks and cuts slots. Since the marks meet exactly at the join line, the slots are also closely aligned, and you get precision alignment at assembly my making sure that the pencil marks form straight lines before clamping.
That said, biscuit slots do not need to be precisely aligned side-to-side. The biscuit fits somewhat loosely in the slots. It's up to the builder to make sure that the pieces are properly aligned at glue-up. This is entirely different from using, for instance, dowels. There, the dowel-drilling phase requires extreme precision both vertically (to get the faces aligned) and laterally (to align the pieces horizontally). Biscuits make the process easier by dividing the issue into two steps. The bed of the BSCM makes the vertical alignment of the slot easy, while lateral precision is done at assembly. Rather than one operation which requires high precision in two axes, it uses two operations which are precise in one axis each. Given the lubricating quality of regular wood glue, it's relatively easy to make fine adjustments at glueup - the problem is making sure there is no shift as pressure is applied.
Although the biscuit fits loosely in the slot, it is made of dried wood which expands as it sucks up water from the glue. This causes it to force the two pieces into vertical alignment, aided by the lubrication I've mentioned. And, in fact, this can cause problems of its own. If you join two pieces of flat stock in order to make wider piece, the expansion of the biscuit can cause the wood to bulge at the biscuits, especially with thin stock. Of course, you can sand the areas flat - but if you do this immediately after glue-up, the excess water from the glue will eventually get dried out, and you'll get depressions at the biscuits. It's not a problem with thicker wood, but you might keep it in mind for thinner.