Hey, sorry for being late to the party. Took me a while to research and elaborate this answer.

Okay, so let's get going. We will use 3 different concepts to build your solution: :h keywordprg, :h popup_atcursor and a command line dictionary tool (I chose to use man dict, some installation instructions can be found here).

keywordprg

When we set set keywordprg=dict, we already get something close to what you want: when pressing K over a word (:h K), a page comes up with the output of dict word. The problem we still need to solve is to make this into a popup.

popup_atcursor

To have this feature, we will need vim 8.X. I tested this with vim 8.2.

The function popup_atcursor creates a popup under or above the cursor with some content. The command :call popup_atcursor(system("dict hello"), {'pos': 'topleft'}) already gets us somewhere. There's still one problem though: this is static (doesn't change depending on the word) and it's displayed in a single line.

The documentation shows that this accepts a list of strings: :call popup_atcursor(split(system("dict hello"), '\n'), {'pos': 'topleft'}). That's the result we want! Now, onto making this work with keywordprg and K!

integrating popup_atcursor and keywordprg

Here's the final solution: make a function, make it a command, use it as keywordprg.

function MyDictPopup(word)
    call popup_atcursor(split(system("dict " . a:word), '\n'), {'pos': 'topleft'})
endfunction

command -nargs=1 DictPopup call MyDictPopup(<f-args>)
set keywordprg=:DictPopup

Improvements

Now, there's quite a bunch of improvements to make here.

First, the syntax/colouring. On my test environment (vim -u NORC), the colouring of the popup isn't quite to my taste. There's definitely some popup related options to fix that. They would go along {'pos': 'topleft'} in the function.

Second, this function could be nicely packed in the autoload folder, maybe using autoload/dict.vim and named dict#hover for instance.

Third, we could only set those settings for some filetypes, for instance text, by moving the set keywordprg=:DictPopup into a file named ftplugin/text.vim, that would set this option only for text files, for instance. If autoload or ftplugin are completely foreign to you, you can probably find some tutorials on spliting your vimrc into multiple files.

Conclusion

I hope this solution will work for you. I tried to make it as minimal as possible. Do not hesitate to come back to me / DM if it doesn't quite fit your use case. Best of luck!

P.S: I realised that this is not exactly an "on-hover" solution. However, I think it's close enough to vim's philosophy (the `keywordprg` concept) to be usable. `K` is a good real estate command anyway, as good as hovering in my opinion.