Learn Swedish: Ingendera laget vinner, medan båda får en poäng. - Neither team wins, whereas both get one point.

Standard negative words like ingen take the indefinite form (like inget lag). However, the dual words from this lesson (ingendera, vardera, and endera) are special: when placed directly in front of a noun, they require the definite form. So it must be ingendera laget.

Since lag is an ett-word (ett lag), shouldn't the pronoun be intetdera or ingetdera?

Strictly speaking, yes! The traditional neuter form is intetdera (or the modern variant ingetdera). However, in modern everyday Swedish, ingendera has essentially become a fixed word used for both en-words and ett-words. It is very common and completely acceptable to say ingendera laget.

How would I say this if I wanted to use the exact phrasing "neither of the teams"?

You would use ingendera followed by av and the definite plural noun. That gives you ingendera av lagen, which means exactly the same thing as ingendera laget.

Does medan mean "while" in the sense of time here?

Not in this sentence! While it frequently means "while" in a temporal sense, medan is also the standard word for "whereas" to show contrast. Here, it contrasts the fact that there is no winner with the fact that both teams still get a point.