Actually, SEGA funded both Zillion and Evangelion (mostly all of the promotion material). You can even see a Mega Drive in the second one.
This Love Live! collab is a "friendly" collab with Bamco, in the same way that Kadokawa is allowing SEGA to make a Kancolle Arcade game.
Offtopic: Those last Evangelion chapters were maded like that because ,with every episode from the start, Gainax invested more money in each episode until some few episodes cost the triple of the estimated! and they almost got bankrupt (Well, the producer went to jail after he did a tax evasion)