I can use Alt-X to enter Unicode on an old machine. How is this possible?

The standard ways to enter Unicode characters on Linux are

• Hold Ctrl+⇧ Shift and type u followed by the hex digits. Then release Ctrl+⇧ Shift.
• Enter Ctrl+⇧ Shift+u, release, then type the hex digits, and press ↵ Enter (or Space or even on some systems, press and release ⇧ Shift or Ctrl).

https://en.wikipedia.org/wiki/Unicode_input#In_X11_(Linux_and_Unix_variants)

Alt+X is supported by many applications though, like MS Word, Wordpad or Libre Office. Therefore I think you've used Libre Office on one system and type on some random textboxes on the other

However using typing the Unicode code points is just for typing rarely used characters. It isn't a good way for typing common characters. You should create a keyboard layout for your own that and access those special characters through AltGr. Even better, you should use LaTeX which is more suitable for scientific documents. You can get any symbols easily with beautiful formatting and don't need to remember the Unicode code points