Most browsers do not allow the mouse cursor to be hidden when screen sharing. For gaming, this can be am obvious problem. Instead, you can use OBS to capture the game and use the OBS Virtual Camera to share the screen with OBS.Ninja that way.
You can setup the OBS Virtual Camera to output a specific scene or screen-share, rather than the current active scene, using this filter: https://obsproject.com/forum/resources/virtual-cam-filter.1142/ If you prefer not to use OBS at all, there are numerous screen-sharing tools that can turn your screen into a virtual camera. Below is a link to a free one for Windows:
Eventually cursor-visibility control will be available for Chrome, but for now, it will be a bit more hassle.