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.
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.