Remember: in this transaction, the output addresses are actually scripts.
For this particular output script, we can read it as “This amount can be redeemed by the public key that hashes to address X, plus a signature from the owner of that public key.” So this brings us back to Script.
Do you have a better idea of why Bitcoin connects inputs and outputs through scripts? Rather than just connecting public keys together, connecting inputs and outputs through scripts allows for potentially complex transaction types.
The Script language is stack-based, has a native support for cryptocurrency, and is purposely limited in capability for security reasons.