Hi, I had a look at the webpage and clicked on Who We Are. Straightaway, I recognised the group. It's the Worldwide Church of God, a non-pentecostal group. Personally, I wouldn't engage in any dialogue. As the blowthetrumpet webpage says, the WCG split several times after the founder's death. I also know that members of their church are expected to follow strict laws, including compulsory celebration of the Feast of Tabernacles (same time as Harvest). I think they believe in/practice speaking in tongues.
Up to five years ago, they had no connection with evangelical/charismatic churches, but one of the groups has since joined the Evangelical Alliance.
I hope that answers your question.