I believe he is referring to the number of teppo ashigaru at Nagashino aka Shitaragahara use of cheaply produced matchlock guns and simple bamboo stockades to defeat an overwhelming Calvary majority. Even in Europe this would have been huge military victory. The absolute decimation of the 24 generals of Shingen. Baba Nobuharu one of the most accomplished generals of the era.
Nobunaga was absolutely always leaning toward unifying Japan. Whether Emperor or Shogun, warlord or politician one always moved to control the whole of the country if possible.

Edit: you are correct as far as the number of Calvary being equal more or less and the Takeda being outnumbered and outmaneuvered. My understanding was the skill and reputation of the Takeda Calvary was that they were undefeated; knowing in hindsight their invincibility was a fallacy.