Even though this animation is very well-known and the narrator says it is "... an accurate representation of the actual DNA replication machine ...", be very careful of its visual appeal. It is, after all, only a fancy animation for educational purposes. Some aspects of the process are shown correctly, but many are simplified, omitted or prettified, and can thus be misleading.
For example, a key ingredient not being shown in this animation (for obvious reasons) is water. DNA and the accompanying proteins do not float in free space, they are immersed in water. But not only that – intracellular molecular enivornments are far more crowded with other proteins than shown in the animation. See for example this whole-cell 3D model of a Mycoplasma bacterium.
Molecules don't know where to go. They move randomly1, bump into other molecules, and generally tend to disperse evenly across the solution. If you put a little drop of food color in a glass of water, it will eventually spread throughout the water. The same "force" drives macromolecules (such as enzymes shown in the animation) to move around. But when two molecules which are somehow "compatible" just happen to by chance come very very (!) close to each other2, molecular forces can help them position in the right way and stick them together. You can watch a simulation3 of molecular dynamics showing a small molecule finding its way into a large protein.
Although your hypothesis about some (mysterious) ions signalization and electromagnetic attraction is somehow reasonable, this is not the correct explanation for the process in animation4. First, electric forces in solution with ions are weak and short-ranged due to screening. Second, they could not be specific enough to attract only some molecules and not the others.
I put some keywords such as Brownian motion, diffusion, macromolecular crowding, molecular dynamics ... with links in my text which you can use to start exploring the topic of physical biology. Any textbook on cell biology or physical biology will be a good start, but the choice very much depends on your prior knowledge.
Oh, and the two-legged proteins are molecular motor proteins.
1 There is also a directed transport of substances inside of a cell, but this is a different phenomenon.
2 Macromolecular crowding actually hinders the movement (diffusion) of molecules around the solution (smaller diffusion coefficient), but it helps them stick together (larger binding constant).
3 Mondal et al. (2018)
4 Moving along a gradient of some chemical does happen, but it usually involves membranes or it happens at larger scales.