A more in-depth quote is later in the article: "Once a device is enrolled for a specific Web site that supports Security Keys, the user no longer needs to enter their password at that site (unless they try to access the same account from a different device, in which case it will ask the user to insert their key)."
The parenthetical seems to imply that they're doing initial auth (and thus cookie generation) with password + U2F, and then re-validating U2F for specific actions / periodically without re-prompting for the password, similarly to how GitHub prompts for "sudo mode" when you do specific account actions.
They support x509 certs, which use PINs. Whether it needs the PIN once-per-session, once-per-15seconds, or once-per-use is configurable. The number of failures before it locks is also configurable. More details can be found here: https://developers.yubico.com/PIV/Introduction/
They also support TOTP/HOTP, where the computer asks the device for a code based on a secret key that the device knows. This can require a touch of the button.
EDIT: TOTP/HOTP modes do support a password, as cimnine pointed out. I'd forgotten about that setting.
Yubico OTP is similar to TOTP/HOTP, and is the mode where the yubikey emits a gibberish string when pressed. The string gets validated by the server against Yubico's servers. This does not require a PIN.
The U2F mode does challenge/response via integration with Chrome and other apps. The app provides info to the USB device about the site that's requesting auth, then you press the device and it sends a token back. This is critical to the phishing protection: barring any vulns in the local app (which have happened before), you can't create a phishing site that will ask my Yubikey for a challenge that you can then replay against the real site. This mode requires physical touch but no PIN.
Thanks!
The PIN is used to configure the YubiKey itself.
> Google has not had any of its 85,000+ employees successfully phished on their work-related accounts since early 2017, when it began requiring all employees to use physical Security Keys in place of passwords and one-time codes, the company told KrebsOnSecurity.