Chat: Open: XMPP, Jabber, Adium, Tox, Jitsi. Closed: WhatsApp, Facebook Messenger, Apple Messages, Line, Skype, WeChat.
Social: Open: ? pump.io, Diaspora? Closed: Facebook, Google+, LinkedIn.
App Stores: Open: F-Droid. Closed: Apple App Store, Google Play
Authentication: Open: FreeOTP. Closed: Authy, Google Authenticator
Office: Open: LibreOffice. Closed: Microsoft Office.
Cloud: Open: ? buddycloud, GitLab. Closed: iCloud, Dropbox, Google Drive, Microsoft OneDrive.
OS: Open: Unixes. Closed: OS X, Windows
Browsers: Open: Firefox. Closed: Chrome, Safari, IE
Maps: Open: OpenStreetMap. Closed: Google maps, Apple maps
I realise these are mostly not "protocols" (depending on what layer we're talking about). Nevertheless, can hardly say that "Open protocols are already much larger than closed systems".