Formatting inconsistencies between vim and other text editors

First of all, I know vim is a text editor and not a word processor, but...

I have a heavily formatted resume in pdf that I want to make as
machine-readable as possible yet decently readable by a human.

I have converted it into plain text first, then, in vim:

:set textwidth=80

I selected the text with "V" and applied "gq". Then I've removed all
formatting and put a bit of spaces and tabs here and there.

It looks great in vim, but when I view it in Pluma, Gedit or Xed
(Debian Stretch) the formatting is all messed up. Some line breaks are
not recognised; tabs are not implemented consistently.

Where would I start troubleshooting the issue? Have I followed the
wrong workflow?

--
Ottavio Caruso

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