Back at I/O 2017, we were promised visual responses from Google Home on a Chromecast and we've been waiting for months for them to show up. A few weeks ago, the first one started working: you could ask Google Home to show you the weather on your TV and instead of answering with the forecast, it would invoke your connected Chromecast and show the weather on the TV. Now the same is happening for YouTube video results.
Ryne tested it by asking Google Home: "show me Aqua Teen Hunger Force videos on YouTube on my Chromecast" and he got multiple video results and thumbnails as an answer on his TV. Previously, Home would automatically start playing the first video and not give you the option of seeing multiple results. This isn't consistently working for everyone, so you may want to test it a few times to see if it works for you depending on your location, language, Chromecast generation, Home firmware version, etc, etc, etc... You get it, there are many variables and knowing for certain when/where it will work and when/where it won't is impossible until Google publishes an official support page for visualizations (and even then...).
Technically speaking, you should be able to follow up by saying, "Ok Google, play the third one," for example, and you may be able to truncate the command to just, "show me xyz videos on my TV/my Chromecast," but further testing is required and I can't do that since I have an Android TV and those are the abandoned children of the Home integration... half of the commands don't work on them.
Google's support page is now live and it explains that you can say "show me x videos" then "play videotitle" to make this work. You can also say "show me what's trending on YouTube" or "show me what's on YouTube." In order for this to work, it requires a Chromecast 2nd gen or Ultra running Cast firmware 1.28 and above and a Google Home. It won't work with Android TVs, TVs with built-in Chromecast, or Chromecast 1st gen.