Actually make URIs "clickable"

You can define .sublime-mousemap bindings, you just need to assign a command to an action like you do with keybindings.

Here are a few examples: Default (Linux).sublime-mousmap, some comment of mine.

[AmjadHD]

That doesn’t work for me, if the cursor is not already on the url, but this does:

{
  "button": "button1",
  "count": 1,
  "modifiers": ["alt"],
  "command": "open_url_under_cursor",
  "press_command": "drag_select",
}

[FichteFoll]

You may also be interested in https://github.com/jfcherng/Sublime-OpenUri (a fork of https://github.com/vicke4/open_in_browser), which shows clickable phantom views that you can click on next to each url and also has lots of settings.