note "rugal in mugen"; in mugen, he is given the nickname "社長"(president).
his special technique, the gigantic pressure, which grabs the opponent and brings to the end of the screen is popular among fans. thanks to this technique, he is called "運送"(the shipping agent). so his nickname means that "he is the president of Rugal shipping Inc.", among mugen fans.
It depends on each author. I regard their relationship as "good friends" or "the trade".
at least, they are good pairing. in mugen, when they divide their roles into "forward" and "rear", they become unstoppable. if opponents defend themselves from yukari's danmaku, rugal will ship. if opponents jump to evade yukari's danmaku, rugal will meet with genocide cutter.