So while Makai Senki is written in English, we can probably figure out what it means. Normally Makai means "underworld" or "realm of the demons":
魔界 【まかい】 (n) world of spirits, hell
But in Garo, Makai might mean something slightly different since the kanji is changed:
魔戒 In this case, it combines "magic/demon" with the kanji for "commandant". Given how they use it, apparently it's anything related to the Makai and can be put in front of as many things as Batman can with the word "Bat".
Senki is a bit harder since we don't know what they're going for. Sen is probably for "war/battle", but without knowing the creator intent, we can only guess at what the second kanji is:
戦旗 【せんき】 (n) battle flag
戦機 【せんき】 (n) time for battle, military secrets, strategy
戦記 【せんき】 (n) military history
My guess would be the last one, which can also be translated as "chronicles". 魔戒戦記 Makai Chronicles would be a fitting, legendary sounding name for a story set in the Garo universe.