Every Google product, whether it’s for the web or for Android, supports Chromecast. Android has system wide support for the Chromecast and you can cast your entire screen to your TV or monitor. The Chrome browser has casting support built in as well so that you don’t even need the dedicated Google Cast extension to cast your desktop or a Chrome tab. It’s therefore surprising that Google Drive for Android lacks Chromecast support. If you have movies stored in your Google Drive, you can’t cast them from inside the app. There are plenty of alternatives of course; you can use apps that can read data from a cloud drive and cast it to your Chromecast. You will of course experience considerable lag if you do so. A much simpler solution is to use the Photos apps instead which supports Chromecast.
Open the Google Drive app and look for the video you want to cast. Don’t tap the video’s thumbnail because that will play it inside Google Drive. Instead, tap the more options button and tap ‘Open with’. If you have multiple apps installed that can open the file you will be asked to choose which one you want to open it with. Choose the Photos app.
When the video opens in the Photos app, there will be cast button at the top right. Tap it to cast the video.
Using Photos over other apps is the main trick here since it has direct access to the files in your Google Drive. Other apps will first connect with Google Drive, likely convert the video, and then cast it, making for a poor viewing experience.