The code snippet you supplied just gives a list of previously created event tags. Ok, this I can probably change to just an input text field so that the user can insert any event tag text to the event.
But I got stuck when you say hook into the "em_event_save" filter, where do I do this? in events-manager.php? Also event tags comprise of several db tables "wp_terms", "wp_terms_taxonomy" and "wwp_term_relationships", and inserting tags related info into these table together, is a bit more complicated than the styles example in the online tutorial.
Amittedly I'm new to wordpress, and for the benefit of others that will surely in future encounter this issue can you please give a bit clearer instructions on how to allow users create their own event tags. I will surely be grateful man