As Andreas says at 0:43, in this video he is talking about a single key paper wallet, which is essentially a piece of paper containing a single private key and single address. I tend to agree with him here; such wallets are outdated. I have several wallets which I would refer to as a paper wallet, that is, a wallet which is generated on an airgapped device using a live OS, stored only on paper, and then all digital traces of the wallet are destroyed. However, all my such wallets are HD wallets, which involve me writing down a seed phrase, maybe a passphrase if I'm using one (on separate paper), and noting the first handful of addresses with which to receive coins. This avoids all the issues with single key paper wallets, such as making mistakes when handling individual private keys, privacy implications of reusing the same address, losing change, and so on. It also allows me to bypass using a printer altogether and hand writing the seed phrase and passphrase instead of printing the private key.

His arguments regarding hardware wallets are also correct, though. For the vast majority of users, a hardware wallet will be a much better option than an airgapped device, since they do not have the technical knowledge or skills to properly set up an airgapped device. No reason you can't combine the two though, if you really want to use a paper wallet. Take your hardware wallet, generate a new seed phrase, write it down, get the first address to send some coins to, and then wipe your hardware wallet. You now effectively have an HD paper wallet.