I'm sure someone is going to Ngram this, but let's go with what you can find through Youtube: walkthrough is the most accepted version.
I'm often mystified by this particular threefold thing as well, because my native language has only one kind of compound word. English, however, has three.
Closed = walkthrough
Hyphenated = walk-through
Open form = walk through
In this case, walkthrough is the correct one. The why is a lot more complicated, and I for one am somewhat confused coming from a closed compound language. Even my spell check on this page is telling me that "walkthrough" is wrong, even if it is right in this sense.
The matter of the fact is that blue-green instead of bluegreen is correct, walkthrough is correct, non-caffeinated instead of uncaffeinated --
The general rule with compound words seems to be to a point arbitrary (which languages are as an excuse for not being universally the same); there is a certain agreement among certain house rules as to what is right and what isn't correct. Walkthrough seems to be the accepted compound rule amongst modern users.
Now, I'm no grammarian. But this manner of thing seems to be arbitrary in prose as well as academia.
Edit: walkthrough is correct due to it being the most used form. It doesn't make sense to me either, but it is purporting to be in essence a guide on how to walk through something.