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Broadcast means an over-the-air on public airwaves and typically also implies a huge viewership, definitely so in 1999.

The Sci-Fi channel was a cable television station and therefore not a "broadcast" station.

However, broadcast can also mean, in a general sense, to air a show.

I'm speculating here, but saying you will pay someone residuals if you "broadcast their show" may not have been a term that was equally understood by everyone. The writer and NBC both seem to have interpreted that term differently, to an amount that means nothing to NBC and a lot of money to an individual person.

Unrelated but I find it amusing that your “however” sentence uses the definition “to air a show” that is clearly a reference to broadcasting something using air as a medium but in this context you were using it more broadly to include both air and cable.

Presumably "Broadcast episode" means an episode shown on broadcast TV, which means "transmitted via radio waves" and is distinct from cable TV (channels only available via cable TV)

I am guessing that broadcast means 'over the air' and Sci Fi Channel is on cable. So they were not 'broadcast'. His contract was per 'broadcast' episode.