There are actually about 3-4 files that make up this listing. The one that you looked at, tpl_modules_product_listing.php, and tpl_columnar_display.php.
It is the last one that lays out the single product per row. You would have to clone this(as it is used elsewhere) rename it, and change the other files to look for the new file.
A bit of work but not impossible. this is tabular data and uses tables, You will most likely lose the control through the admin for this display so lay it out as you want and you can leave out the check for this or that switch else stuff



