The Act defines place of public accomodation. There's no way you can fit an "app" into it. There may be subsequent laws or decisions that make such discrimination legal, but the law he quoted is NOT it.
(b) Each of the following establishments which serves the public is a place of public accommodation within the meaning of this title if its operations affect commerce, or if discrimination or segregation by it is supported by State action:
(1) any inn, hotel, motel, or other establishment which provides lodging to transient guests, other than an establishment located within a building which contains not more than five rooms for rent or hire and which is actually occupied by the proprietor of such establishment as his residence;
(2) any restaurant, cafeteria, lunchroom, lunch counter, soda fountain, or other facility principally engaged in selling food for consumption on the premises, including, but not limited to, any such facility located on the
premises of any retail establishment; or any gasoline station;
(3) any motion picture house, theater, concert hall, sports arena, stadium or other place of exhibition or entertainment; and
(4) any establishment (A)(i) which is physically located within the premises of any establishment otherwise covered by this subsection, or (ii) within the premises of which is physically located any such covered establishment, and (B) which holds itself out as serving patrons of such covered establishment.
The 1964 isn't the end all of civil rights legislation. It covers public accommodation and employment and a few other things, but it took additional laws to further outlaw discrimination such as the later Fair Housing Act/Civil Right Act of 1968, etc...