Mark Baker was extremely helpful in guiding me to the right answer. I don't use Composer with PHP (I should probably learn), but given that, in order to get this to work I went to the GitHub page for PHPExcel (https://github.com/PHPOffice/PHPExcel), clicked the green Clone and download button, and then the Download ZIP link.
After unzipping the file, I got a folder called PHPExcel-1.8. I moved that folder to the same folder as both the Excel file I wanted to read (in my code below test.xlsx) and the PHP file that has the code below.
The key to getting it to work was inputting the correct path to the IOFactory.php file. It may seem simple to some, but it was tripping me up.I use PHP-ExcelReader to read xls files, and works great.