If you watched the video of Levi in the back seat of the car asking about "What do we call it when STOP spells POTS backwards?", this scene was an re-enactment. The actual event occurred sometime in February, 2017.
Levidrome was coined later that day when Levi's parents determined that there was no word in any written dictionary for this linguistic phenomenon. He said, "Well then, we should name it after me! It should be a levidrome!" Levi was 5 at the time.
It was later confirmed when Levi's dad, "Lucky" Budd, contacted Webster's on Feb 19, 2017. Webster's got back to Budd to confirm that there was no word in their dictionary for this and a bit about how a word gets into the dictionary (explained in the YouTube video)
So levidrome was created and shared within the Budd family in early 2017. It wasn't until later on in the year when they released their video and unleashed Levi's word onto the internet.
Let's make this happen!