Yes, the Christians I am talking about believe in predestination, and they disagree with, for example, Baptists about whether people can save other people or whether people can save themselves. Instead they believe God predetermines who ends up being saved or not, through the grace of God alone.

And to answer your question about what is the ultimate point if there is no motivation through free-will, their answer is usually either "it's a mystery" or "to glorify God".

They still believe in a kind of free-will, but only within the confines of God's pre-determined choices. God chose for you, but it was you that did the choosing and are responsible. One explanation I was given is that you make the choice out of free-will, and then God observes your choice and then goes back in time and determines it from the beginning. It's not a coherent view, as far as I can tell - there is no compelling logical or reasonable compatibilist account they offer, it just sounds like contradiction and fantastic thinking.

Also, their view is that our nature is fallen (total depravity), and the only good is from God and God chooses who receives the gift of salvation and thus who will become cured of their evil nature. They believe they should do good things and proselytize to convert others to Christianity because God commands them to, not because those things will save themselves or anyone else. Obedience is very important to this mindset.