Trump himself has referred to changing administrations. Purposely not saying the word "Biden", he meant interpret this as from Trump term 1 to term 2.
Second sentence is just a general statement of truth, without being specific or judgemental.
I'd like to go to Castor's actual words and context, but I suspect, as usual, this is AP dreck trying to make news that soothes the left and angers and divides the right. I'll note that the "He added..." part is meant to take separate thoughts and combine them to make them more speak to AP agenda.
NO, it is absolutely not! The American people DID NOT just pick a new administration unless you think the election was results are legitimate, which they ARE NOT!