Kirjastokaista is WordPress based website, and therefore it can offer an API for developers. Data can be queried by using WordPress JSON API.
Instructions on using the API can be found on its website:
http://wordpress.org/extend/plugins/json-api/
Some query examples:
List category IDs
10 newest videos
10 newest videos that have been marked as finnish
Search by keyword “ifla”
1 video randomly from category 18206
Kirjastokaista’s videos transfer from Vimeo, which also has an API ja widgets.