Workaround:
Set ClickToOpen = true in the control markup or if you want to set it only for the problematic browsers, use the following server-side code:

    protected void Page_Load(object sender, EventArgs e)
    {
        string userAgent = Request.UserAgent;
        string searchPattern = "ARM(?i)|Touch(?i)";

        if (System.Text.RegularExpressions.Regex.IsMatch(userAgent, searchPattern))
        {
           RadContextMenu1.ClickToOpen = true;
        }
    }