Only officially-licensed games released in North America or Europe need to be completed, including standalone eReader games.
Games that can be finished (i.e. "the end" or "congratulations" screen or end credits) must be completed.
Anything beyond "the end" screen or end credits is optional.
A game can be marked as completed if every single avenue to victory has been explored and it appears there is no way to beat it due to a bad design or a bug. Otherwise it has to go on "abandoned" status (see abandonment rules).