TL;DR: He compares one hour worth of transaction blocks, not six blocks. I.e. he compares the security of 6 blocks in the bitcoin network opposed to 24 blocks in the litecoin network.
In the video the host reads from a sheet with calculations that is supposed to prove that Litecoin is more secure than bitcoin. The calculation is based on the assumption that a 51% attacker wants to mine one hour worth of blocks with 35% of the mining power. Finally, he concludes that 8 transaction blocks in the litecoin network offer a similar security as 6 blocks in the bitcoin network. I.e. block to block litecoin isn't securer than bitcoin, however it reaches the same level of security in less time.
I can't comment in how far the presented numbers are factual (I didn't repeat the calculation), however I am not convinced of the conclusion "litecoin is magnitudes more secure than bitcoin". A 51% attack does not require an hour worth of blocks, but rather a specific number of blocks, in which even the host tells us that Bitcoin is more secure.