It's a two-part claim; a) yes, conversational AI agents will replace typing searches into a text box, but b) I see no reason to think that Google can't easily monetize that format.
Regarding the first point, I think Google appears to have been caught a little bit off guard as to how soon this transition would happen. People seem to be over-indexing on the "code red". I do think it's a strategic mis-step by Google to not have a product ready to go here. (Their broader strategy was quite risk-averse and that was probably sensible, given the shit-storms that previous systems like Galactica and Tay generated; Google couldn't be the first ones to publish a prototype/demo system like ChatGPT, or the NYT would have jumped all over them for the inevitable questionable utterances.)
But the second part; given AI agents are here, who's going to win the competition to monetize them? It seems clear to me that Google is in a great place to monetize and capitalize on this technology, and I think they will win if their language models are better. (So far, they seem to be way ahead; LaMDA was early 2022, and it's clearly better than ChatGPT.) If Google's version of this service is substantially better, but intersperses ads based on what you're talking about (the Gmail model for ads), would people use this? I think it's clear that consumers would take the better free service that comes with ads, vs. paying ChatGPT or accepting inferior quality.
Let alone the fact that Google can put the assistant onto billions of Android phones, fine-tune a model per user, offload compute power with device-based inference to save OpEx, and so on; all of these will give whoever is running the AI agent a lot more ad targeting power.