I was watching the following video and I started wondering why the rounds seem to explode after a certain distance. I'm assuming it's slower-moving tracer rounds being hit by faster, follow-on non-tracer rounds. But if that were the case, why wouldn't we see it all along the stream of fire?

It doesn't fire bullets. It fires 20mm high explosive incendiary tracer shells. And these are equipped with a self destruct feature that causes them to blow up after traveling about 7500 feet, to prevent all the shells that miss the incoming target from falling to the earth further away and inflicting unintended damage or casualties.

Thank you, sir!