First things first: there is no Import/Export function! You need to perform the movement manually with the following steps:
- install the same version of Event Gallery on both sites
- recreate your tags and categories
- copy your image data. You find it in /images/eventgallery
- export the database table #eventgallery* and import them to the new database
- Adjust categories and events. In the previous step, you recreated them. They have new IDs. Open each Event, assign the new categories and tags and safe them. You can try to use the batch function for Events.
- If you get messages about missing users, please use SQL to fix this in the #_eventgallery_folder and #_eventgallery_file table. The IDs in the column userid need to be valid user ids.