The chemical reaction that is being visualized in this video with a fluorescent dye actually changes the surface of the egg. Prior to fusing with a sperm, the egg has proteins on its surface that match proteins on the sperm surface (like a key and lock). Once the sperm protein fuses to an egg protein, the egg protein changes shape. That shape change causes a chain reaction across the surface of the egg. After that chain reaction, the egg surface proteins no longer match the sperm proteins.
It is possible for two (or more) sperm to fuse with the egg simultaneously. Eggs fused with more than one sperm will not develop any further.
When I first learned the basic process when I was about seven or so (how did the baby get in there?), I never thought to look into it further. I thought about my own creation that God must have picked just the sperm he wanted and caused it to penetrate the egg. That's pretty naive lol.