Thus, if a TreeViewNode is tapped on a mobile device, the context menu will be shown. And on desktop, the context menu will continue to be shown on right click.

As a workaround, you may handle the RadTreeView OnClientNodeClicked event as follows:

OnClientNodeClicked="ShowContextMenu"

<script type="text/javascript">
    function ShowContextMenu(sender, e) {
        if ($telerik.isTouchDevice) {
            sender.showNodeContextMenu(e.get_node(), e.get_domEvent());
        }
    }
</script>