Start-Process is a PowerShell cmdlet, and so it must be executed at a PowerShell prompt, but the BatchPatch remote command features execute at the Windows command prompt, so you must invoke PowerShell first for PowerShell cmdlets to be executed. Tutorial here:
https://batchpatch.com/executing-powershell-commands-on-remote-computers-with-batchpatch
With regard to launching Chrome or any other interactive process or application, you need to be aware of a couple of things.
1. The remote process will be launched in the context of the user account that you use the launch it. This won’t necessarily be the account that is logged-on interactively at the target computer. The process won’t be visible/interactive if the accounts don’t match.
2. Even if the accounts match, the process will generally still be hidden, though in some cases for some processes you might be able to launch them interactively if you use the ‘interactive’ switch. See ‘Tools > Settings > Remote Execution’ and set ‘Elevated token + Interactive’. This is the only remote execution context setting for what you are trying to do that *might* work. It might not though, so you’ll need to test.