Word Table Form - Adobe adding form fields where not needed

We don't know the exact logic behind the fields detection wizard, but it's likely it's picking up the borders of your table and adding fields based on that. The results of running it are never going to be perfect, though. You'll always have to go in and fix them manually. In your case it did a pretty good job, actually. You just have to remove those extra fields, which shouldn't take too long. I've seen much (much) worse results, to the point where it's not worth trying to fix them, but better to do everything from scratch.

It is possible to add fields using a script, though, and then you get much more reliable results (also because you can control the algorithm behind it). For example, I've developed two (paid-for) tools that will add fields based on characters on the page. The first creates check-boxes or radio-button fields based on certain Wingdings characters and the second will create text fields based on sequences of underscore characters. They both work with 100% accuracy and allow you to define the exact locations of the fields when designing the file (in Word, say).

You can find them here:

https://www.try67.com/tool/acrobat-reader-convert-wingdings-characters-to-check-boxes-or-radio-buttons

https://www.try67.com/tool/acrobat-reader-convert-underscores-to-text-fields