You are missing Tags
and WT
elements in your query:
string val1 = xdoc.Root.Element("Tags").Element("WTs").Elements("WT")
.Where(q => (string)q.Element("ID") == "ID_1")
.Select(q => (string)q.Element("Value"))
.FirstOrDefault();
Or simply look for descendatns
string val1 = xdoc.Root.Descendants("WT")
.Where(wt => (string)wt.Element("ID") == "ID_1")
.Select(wt => (string)wt.Element("Value"))
.FirstOrDefault();
XPath solution will look like
string val1 = (string)xdoc.XPathSelectElement("//WT[ID='ID_1']/Value");