Learn Dutch: Loopt nogal uit, ben vrij laat. - Is running quite late, am pretty late.

This is an example of "topic drop," which is very common in casual spoken Dutch or text messages. The speaker is omitting the unstressed subjects at the beginning of each clause. Fully written out, it would be Het loopt nogal uit, ik ben vrij laat. Because those pronouns are dropped from the very first position, the phrases end up starting with their verbs.

What exactly is running late, and why use loopt uit instead of just is laat?

The separable verb uitlopen specifically means that an event, appointment, or schedule is running past its allotted time. You use it for situations, which is why the implied subject here is het (it). You wouldn't use uitlopen for a person; that is why the speaker uses a form of laat zijn (ben vrij laat) to describe themselves in the second half.

Is there a difference in meaning between nogal and vrij in this sentence?

Both mean "quite," "pretty," or "fairly" and are often interchangeable in Dutch. Nogal can sometimes carry a slightly stronger or more negative tone ("rather late") compared to the slightly softer vrij ("fairly late"). Using both in one sentence is just a natural conversational way to add variety so the speaker isn't repeating the exact same word.

Is it normal to just link these two thoughts with a comma instead of a conjunction?