Everyone in the world (except for Russia, with their 'special operation' euphemism) recognizes the invasion of Ukraine as a war. People are still pretending that Israel bombing targets inside Iran and Iranian military units in other countries, and Iran launching a large-scale missile strike against Israel, isn't a war. It's no longer a proxy war, it's a direct conflict, but because people are still stuck in exactly that mode of thinking- that 'war' means artillery and troops and taking ground- people are treating this as something else.
I don't think the author is correct that war won't still look like the WW1/2 paradigm of conflicts as well, but as of right now there are 16 countries involved in the Israel/Iran not-war:
Direct involvement:
Israel
Iran
US
UK
Syria
Iraq
Jordan
Yemen
Lebanon
Logistical involvement (including intelligence sharing and air defense deployment):
Kuwait
UAE
KSA
Qatar
Oman
Djibouti
Bahrain
I think the salient point is that the US's insistence that they/we're not yet in a war is a lie designed to both avoid blame being put where it belongs (Israel's genocide of Palestinians, and the US's involvement, that kicked this all off), and to temper calls for more action to stop the war, which will require stopping Israel in Gaza.
By calling for preventing a war, the US is attempting to blame future actions, whereas if they acknowledge we're already in a war, they'd have to admit that it's because of actions that already took place, and the US wants desperately to make Iran the bad guys here, and claim this has nothing to do with Israel doing war crimes both in Gaza and in Lebanon.