You likely have nothing to worry about. Phishing relies on tricking you into entering sensitive credentials. It's very rare for it to exploit you directly and if they did want to do that, they wouldn't be showing you a password prompt. However, it is possible that merely typing in your account details sent data to them even if you did not press enter, so you should change your password. I don't think that's likely in this case, since I logged network activity while typing a dummy password into that phishing site and could only see it send it when I actually pressed enter, but it's still a good idea to change those passwords.
It is possible that the page has attempted to use exploits against your browser regardless. Generally, these exploits will be against old browsers or outdated plugins. If you keep your browser up to date, it should not have public security issues that could be used to install malware via a drive-by download.