Go to includes/functions-template.php
All the functions there are so called pluggable functions. You can just copy any of them, paste into functions.php of your theme and modify according to your needs. The copied function will be used instead of the one in the plugin.
In your case you need to modify em_display_events() which is responsible for events list display. There's a standard WordPress loop that starts with this:
and displays the events with the corresponding data like event date, thumbnail, excerpt etc.
All you need is to add a piece of code to display event categories (or anything else you want) as you would do with any other WP query, for example using get_the_term_list function.