smartcookie, there are so many “ifs” in this story.
#1, if he is indeed the sole proprietor and he is in fact a yid, he might be doing the minyan as a service to the neighborhood or because he promised his parent to say kadish for him/her and so needs a minyan whether he is frum or not. So don’t jump to conclusions or judge.
#2, As others said, he might have a goy as a partner or he might be just the manager and not at all the owner.
#3, Even if he is a frei yid, you can’t force a non-frum Jew to be shomer shabbos, and you can’t boycott him for not being Shomer Shabbos. There is no halacha that I know of to keep you from buying from him. Century 21 is owned by Jews and is open on Shabbos, how many Yiddin refuse to shop there? National wholesale liquidators was owned by Jews, did you not shop there? There are many stores that are owned by non religious Jews but there are no boycotts on those stores. It is a personal preference. If you wish to boycott that store, do so. But don’t make a public issue out of it. As he enjoys the support of the community he may then want to hear what the many “friends” he has made might have to say about him being open on Shabbos. Starting a negative campaign will only effect a negative response.