I think there are three things that make worship distinctively Christian.
1. What is done is done explicitly in the name of Christ, the Great High Priest. This can either be done formally (with a signing of the cross whilst saying 'in the name of the Father...') or informally ('we have gathered together in the name of Christ...'). Yet I believe it crucial to do this, not least on grounds of spiritual warfare.
2. That the Scriptures, especially the gospels, are read out loud in the midst of the assembly. Christians are a people constituted by a particular story about a particular person, and to retell the story is a way of recognising that the assembly lies under the authority of Scripture.
3. That there is something sacramental in the worship. Normally this would be the Eucharist but it could be Baptism; more broadly it might include anointing and the laying on of hands, or be a marriage. I see this as essentially Christian as it reflects the logic of the incarnation: Jesus wasn't just a teacher, he embodied the truth. In the same way Christian worship is not simply about speaking or hearing truth, but about being formed to perform the truth. Sacramental worship achieves that.
There are many facets of Christian worship - such as creeds, confession, intercession - that help to fill out the nature of Christian worship but I believe that where these three elements are present then we have fully Christian worship. This is why Holy Communion is 'the source and summit of Christian life' and 'the richest and fullest expression of Christian faith'.
It is certainly possible for worship to miss one or two of the above and still remain recognisably Christian (eg Morning Prayer). However, where a community does not have regular access to the full expression of Christian worship then it begins to drift away from the fullness of the faith. This has happened, I believe, with organisations like the Salvation Army (however highly esteemed they deserve to be on other grounds).
Where worship lacks all three of the above elements then I doubt whether it qualifies as Christian. This is one reason why I was so disturbed by the worship offered at New Wine; it was, at best, sub-Christian.
Tomorrow I want to say something about the participation of the believer in worship.
Other posts in this series:
Participation and Performance
Worship is useless