｢悪魔城ドラキュラ 闇の呪印｣が元となっています (Pachislot Akumajo Dracula is based on Curse of Darkness). ラルフ側から見たもうひとつの物語が､ パチスロ版の悪魔城ドラキュラI･Ⅱのストーリーとなっています (Pachislot Akumajo Dracula I&II story is a "gaiden" from Ralph's perspective.)
The way the word "gaiden" is used suggest that it means "alternate timeline".
It actually says "another story" (もうひとつの物語 / Katakana: アナザーストーリー) which is a synonym of gaiden. "another story" is a loan word of sorts from English but I don't think the term is actually used in the west. The "another" part refers to a story taking place in "another world" i.e an alternate universe.