That could be done yes. Copying the theme code would not be easy, but the layout is actually quite simple, albeit 3 posts to a row.
The issue would be the time it takes and how much you value your time. At the rates most users would value their time, it can be cheaper to buy a page builder plugin. It depends on how good you CSS/HTML skills are.
I do not know what the function that I can see in the code you posted do.
Thinking about it be able to get it to work with search.php, you MIGHT, if you edited the search.php file, be able to add one just extra line, before this line:
codetipi_15zine_main_layout();
try adding this line:
do_shortcode('[searchandfilter id="28099" action="filter_next_query"');