This reminds me of an argument I had with my friend Brendan. He was discussing the difference between a "trilogy" and a "movie in three parts". He said Star Wars was a trilogy, and LotR was a "movie in three parts". He wasn't sure where to place Godfather.
I told him that he was stupid, as a trilogy is defined as:
–noun, plural -gies. 1. a series or group of three plays, novels, operas, etc., that, although individually complete, are closely related in theme, sequence, or the like.
2. (in ancient Greek drama) a series of three complete and usually related tragedies performed at the festival of Dionysus and forming a tetralogy with the satyr play.
3. a group of three related things.
Ergo a trilogy is just another way of saying a "movie in three parts". Oh sure, if anybody else had made this argument I would have given it some merit, but I don't really like this person.
Now, back on topic, I hesitate to call the SoulBlazer Trilogy a trilogy in the way that the Star Wars or LotR movies were, but in the definition we've agreed upon, sure. Ergo, if these Actraiser games are in fact related, then we must expand our meaning to make it a series. (In the same way we grudgingly did when the first three Star Wars episodes came out..)