Is there a Joystick Node?

Sure it does - HTML can have a <script> tag (so can the ui_template)

The function node ran is server (NOT client side / dashboard)

Read the help info and search the forum - it is perfectly possible (and has been covered lots and lots of times - search ui template send message)

the joystick demo runs client side (has nothing to do with node-red). If you make it work in the ui_template (i.e. the browser) and hook up the events to send messages to node red - yes.