Do I need to own a game to make a Workshop showcase?

No. Paste one line into the browser console on the Workshop upload page and the item is posted under Spacewar (app 480), which you don't need to buy.

What does the console line do?

It sets three fields on the upload form: the app to Spacewar (480), the file type to artwork, and the visibility to public.

Why do I have to paste it again for every piece?

Steam clears the form after each upload, so the fields go back to their defaults.

Make a Workshop showcase without owning a game

Steam normally only lets you post Workshop items for games you own. One line in the browser console posts them under Spacewar instead, a free test app everyone has.

Steps

Make your five pieces. The Artwork Maker cuts a clip into five 158×450 GIFs that play as one banner.
Open the Workshop upload page: steamcommunity.com/sharedfiles/edititem/767/3/
Open the browser console with F12, then click Console.

Paste this line and press Enter:

$J('#ConsumerAppID').val(480),$J('[name=file_type]').val(0),$J('[name=visibility]').val(0);

Add piece_01.gif, give it any title, and submit.
Do the same for pieces 2 to 5, in order. Paste the line again each time.
On your profile go to Edit Profile, then Featured Showcase, add a Workshop Showcase, and pick the five pieces from left to right.

If the console won't paste

Some browsers block pasting into the console the first time and ask you to type a phrase to allow it. Type what it asks, press Enter, then paste the line again.

Make Workshop pieces

Questions

Do I need to own a game to make a Workshop showcase?: No. Paste one line into the browser console on the Workshop upload page and the item is posted under Spacewar (app 480), which you don't need to buy.
What does the console line do?: It sets three fields on the upload form: the app to Spacewar (480), the file type to artwork, and the visibility to public.
Why do I have to paste it again for every piece?: Steam clears the form after each upload, so the fields go back to their defaults.