Yes, you need to buy the PC version as well. It is irritating.

Even MORE irritating, though: You need to buy both the PC and PS4 versions to play on ANYONE's PS4 or PC. Accounts SHOULD be platform independent, but they aren't. Registering PS4 lets you play on any PS4 in the world with the software installed. Registering PC lets you play on any PC in the world with the software installed. But you have to choose one or the other unless you register both. It's frankly kind of bizarre.