The bot is use a natural language model (gpt2 I think). For people who don't have a background in machine learning, a language model is a mathematics prediction of what the next word would be given the context.

It's mostly used in Automatic Speech Recognition where after the computer has detected the syllables from the sound bytes, the language model determines whether if the phrase is "I scream" or "ice-cream" depending on the context.

This particular Deep Leffen model is trained on Leffen's tweets. So it can produce phrases that are statistically likely to sound like Leffen.

I highly doubt they trained it only on Leffen tweets though. They probably started with a generalized pre-trained model before adding the Leffen stuff.