The link in the OP is dead. Here’s an example of his standard stuff. There’s another version that has some comments by Tom spliced in. He seems to have stopped doing the bit/gave up smoking over 20 years ago. He does admit that he burned his mouth doing this trick.
I think part of it involves using fakish cigarettes. Designed to easily go out after a few seconds. At times, not a lot of smoke seems to come from the tips, generally from his mouth. (As noted, there are ways to fake smoke.) And he keeps relighting them. The “cigarettes” might also be flexible for easier stashing in his mouth.
He does move his hand down below the table when he throws the cigarettes into his mouth. He could be dousing the end or something.