Email is transferred to its destination (where, sure it might be accessed through a Web UI) via SMTP. Even where things like Slack are used internally, email usage between organisations is still extensive, due to effectively being a federated lowest-common-denominator system that’s not completely at the mercy of a single vendor.
VoIP, which increasingly underlies telephony/mobile networks, uses things like SIP, RTP and RTCP - even if, again, it might be accessed via a Web UI, it doesn’t have to be, and there are dedicated clients.
SSH is widely used for remote system administration. SFTP, built on top of SSH, is used to transfer sensitive data, e.g. (in the US) medical records covered by HIPAA.
SNMP is used for network device management, sometimes doing so via the Internet.
Don’t confuse certain end-user applications with the Internet more generally.