Broadcast networks have to give the different major parties equal time. Since Kimmel only wants to give a voice to one party he cannot use the broadcast network.
On what basis are you saying that Kimmel only wants to give voice to one party?
Also, they do NOT have to give equal time, and "major parties" is not part of it; They have to afford equal opportunities to all other such candidates for that office. IE: if Paxton passes on the opportunity, that doesn't block Talarico from airing.
ALSO, as you implied, the "broadcast network" has to give said opportunity. I see nothing in 47USC315 that says it has to be on the same show.
47USC315 also says, "Appearance by a legally qualified candidate on any ... bona fide news interview ... shall not be deemed to be use of a broadcasting station within the meaning of this subsection." IANAL, but this isn't a paid for appearance, and it is an interview, and it's only falling under this provision because the FCC recently reclassified how late night shows are handled.
There are too many ways in which this doesn't apply or is being applied incorrectly. It's the government strong arming a broadcaster to chill speech.