Japanese people totally are into German/European/Classical/Romantical culture and art, including Beethoven's music which again implies the Moonlight Sonata.
When it's played in either a movie, game or anime (for example it's played in Kaitou Jeanne, both the first and third movement.. on an organ, but well), either love or deep/strong emotions are involved.. But also somewhat of dreaming, longing.

As for your listed games I can't really tell if my reason answers your question as I've never played them.

But there are many other games which feature this kind of music, for example: Clock Tower 3 (PS2) features Chopin's 'Fantaisie Impromptu', and so does -besides many other Chopin songs- Eternal Sonata (PS3/360).