The two things I can think of are:
a) communication protocols that aren't encapsulated in http(s), websockets, or webrtc. There's good reasons for some of this, and it's not that limiting, since popular protocols tend to grow some of these encapsulations to circumvent lazy firewalls, but it sticks out to me. Additionally, a page/app can't run a server for other browsers to connect to, it's got to be intermediated with a separate server; it would be difficult to make an offline LAN multiplayer game work.
b) reliable non-interactive push messaging and/or background connectivity. Again, there's good reasons, and you wouldn't like every page/app to have this capability, but this capability enables good offline usability by fetching data when available and pushing user driven updates when available.
For example, Email should be offline capable, and it should have nearly all the messages that were available when last the device had connectivity, and it should let me compose new messages and replies and queue them until connectivity returns. Maybe it should even speak IMAP and SMTP, but JMAP is probably good enough and browser accessible. Same with other messaging systems, assuming they have queued messages and aren't online only.