If I’m not mistaken, there was a Steelers/Dolphins game a few years back that got moved to Monday night because of weather. The game was only televised in those markets.
The Bills and Jets played a
rescheduled game on Monday night in 2014, as a result of what we now fondly call either "Snowmaggedon" or
"Snowvember". They couldn't play in Buffalo, so the game was moved to Detroit and played at Ford Field on a Monday night. I believe you are correct about television coverage - it was on TV locally here in Buffalo, but I think it was only shown in the local markets of the teams involved.
Fun fact, University at Buffalo was supposed to play Kent State on Saturday that same weekend. The Kent State equipment truck got stranded on I-90 between Erie PA and Buffalo for days; the game was cancelled and never played.