I’ve seen a number of instances where a church or a member of a church claims that their worship “doesn’t use liturgy”.
They seem to mean that they don’t use sung prayers, or set words, or participate in the Eucharist — they avoid The Liturgy Of The Church, so to speak.
I understand liturgy much more broadly: as the shape and format of public worship. Of course, religious traditions that are not Christian have their own rituals and patterns, often their own set liturgy. Context is important.
Where set liturgies exist, patterns of adherence vary; the Church of England typically prescribes the words that must be used by certain people, but allows relative freedom in using different translations of scripture, adding other words, setting words to music, and so on. If you sing the Magnificat to a different tune it is still the Magnificat; if you use a metrical translation and have the whole congregation sing it, it is still the Magnificat; and then the BCP offers an alternate canticle, too (rarely used these days, in my experience).
If you sing the Magnificat to the same tune every day for three years, it could be argued that although that tune isn’t a necessary part of the liturgy prescribed by the C of E, it has become de facto liturgy in your local context. And “30 minutes of the band, 40 minutes of emotive preaching, another 30 minutes of the band” is liturgy, too, if you do it that way every week, even if you decide you are going to say it isn’t liturgy.
I think perhaps a good question to ask to decide whether worship is liturgy is whether someone is going to grumble if you change it.
Whether to use your tradition’s set liturgy is outside the scope of this post: many factors can render a specific liturgy unfit for purpose. But if you’re going to re-invent the wheel, it’s as well to know what you’re doing, and call it a wheel.