As a cat parent, I 1000% agree that cat massages are the best! No $120 massages can compare to your kitty lying on your lower back and purring all your stress away for you.
Calling it Neko no Massageya-san... has to be one of the most peculiar specimens of the mixed-Romaji-and-English transliteration-style that the English scanlation scene has developed over time... XD
...I was wondering what the heck a まっさげ屋 would be. :'p