How do non-deterministic wallets violate the principle of address reuse?
The text indeed doesn't make it's case clear, but the idea is that random key generation makes for inconvenient backups.  The more keys you generate, the more frequently you will have to back up the wallet.

To avoid this, some users of non deterministic wallets have resorted to reusing keys\addresses, as a sort of easy way out of having to follow the demanding practice of frequent wallet backups that are needed when new keys are generated.