If you read Jeroen Lamers, Japonius Tyrannus, carefully, you will quickly realize that Nobunaga's use of the word "Tenka" is not new.
"In short, when Nobunaga's tenka is understood as 'state' rather than as his personal 'realm', it does not seem such a revolutionary term at all. It designated an order headed by an imperial sovereign and effectively maintained by a military hegemon" (Lamers, p. 71)
If you read page 70, the word "tenka' replaces Kyoto. Kyoto means the state when the phrase tenka no tame is coined.
Furthermore, there is evidence to support this. The evidence comes from the Jesuits. Alessandro Valignano describes the Tenka as Kyoto and the five home provinces near the capital (Lamers, p. 70). Home provinces Yamashiro, Yamato, Izumi, Kawachi, and Settsu.
I do agree to a point that Nobunaga's use of the Tenka means the state. However, from the evidence I have learned from Nobunaga's character alone, there is another use. The word Tenka may have been used long time ago from other warlords, but I do think Nobunaga took it to a new level. He used the Tenka for the state as well as his own realm.
Nobunaga no tame!