Most likely the error is because the RadTreeListView is not EXACTLY the same as the object you mapped it to... so, TestComplete is going to have some problems with doing the same sorts of things.
Looking at your property list and your object browser, I think you're going about this wrong. The way that TestComplete is "reading" your component is that the actual items are, themselves, child objects of the tree list view. Notice you have five "TreeListViewRow" objects. I can't be sure, but it seems that these relate directly to the 5 rows in your tree view on screen. To click on an "item" in your tree list view would be to click on one of those child objects, not to call a "ClickItem" method on the tree view itself.
So... what it seems to me is that you should write some sort of script routine that will simulate a ClickItem. I'd use FindChild to find the specific TreeListViewRow object that corresponds to the desired text string/index you want and execute a click on that item. You might need to add code to do an expand of the tree so that you can expand nodes that may be collapsed.
So... undo your object mapping and start down the road of investigating what you have exposed natively. You should be able to find a combination of methods and properties to do what you want built in to the object itself.