Hi Martijn,
The problem is the event categories are not stored as meta data, they are taxonomies. So tribe_get_event_meta will not work in the code you’ve got. To get the current posts taxonomy terms (categories) you’ll need to use a native WordPress function like wp_get_object_terms() – http://codex.wordpress.org/Function_Reference/wp_get_object_terms
That will return an array which you can then tap into like so: https://gist.github.com/3b29a226dc036de93039
This will echo the first value in the array. This doesn’t account for instances where you will have more than one event category assigned to a post. That’s more complex and you’ll need to figure that out on your own.
I hope that helps!