Are non-denominational churches held to any standards to be considered a church by other denominations?

That depends on the denomination. The general rule in ecumenical circles is to let people define themselves. Thus, most Protestant denominations will consider each other as well as non-denominational congregations as “churches” in the broader sense of the word. We Catholics take our lead from the Dogmatic Constitution on the Church (Lumen Gentium) of the Second Vatican Council which proclaimed in Paragraph 8 that “while the Church of Christ constituted and organized in the world as a society, subsists in the Catholic Church…many elements of sanctification and of truth are found outside of its visible structure.” Depending on how many of these elements are present, we make a distinction between what constitutes a “church” and an “ecclesial community.” Because we recognize the validity of their Eucharist and the apostolic succession of their Holy Orders, the Eastern and Oriental Orthodox Churches are spoken of as “churches” in the strict sense. Meanwhile, Protestant denominations are understood as “ecclesial communities.” While it is a subtle, but important distinction for us, it should be noted that such a distinction is not shared, and often not appreciated, by our Protestant brothers and sisters in Christ. A great deal discretion is required.