The claim this author makes is true. To begin with, the author of the article cited, Michael Gold is a real author for The New York Times and has been a political correspondent for them for a while now and has written numerous articles on Trump's 2024 Race. In addition this article is a piece published by the New York Times which is known for their high reliability.
When researching this article, I did find the fully rally speech made by Trump in North Carolina. I did not find exactly when he was discussing the Democrats rigging the election of 2024. However in research the claim that has repeated stating election fraud. I found a New York Times article discussing and finding all the times Trump has denied election results, so the claim the behavior is repeated is true.
Sources:
Michael Gold Linkedin
History of Trump saying the election was rigged
Trump Rally
Trump claims the 2020 election was rigged