There are a number of ways to get which video adapter is installed on my computer, Display Settings, System Info tool, Device Manager, etc. You can even do so via a PowerShell cmdlet.
But how do I get that info from a remote computer?
There is a WMI class called Win32_VideoController for you.
Get-CimInstance -ClassName Win32_VideoController
The property Description reveals what kind of Video Adapter is installed on the computer. And you will find what current screen resolution is by scrolling down the page near to the bottom of the command output and finding out the property called VideoModeDescription.
Now, to get the save video controller and screen resolution info from a remote computer, add the switch -ComputerName:
Get-CimInstance -ClassName CIM_VideoController -ComputerName $computername
If the output is too long to read, narrow down the output by piping the result to Select-Object.
Get-CimInstance -ClassName CIM_VideoController -ComputerName $computername| Select-Object -Property Description, VideoModeDescription
If you need to get the info from a list of the computers, you can either prepare a text file that contains the whole list or simply use something like this:
$list = 'computer1', 'computer2', 'computer3'
Get-CimInstance -ClassName CIM_VideoControllerResolution -ComputerName $list | Select-Object SystemName, Description, VideoModeDescription
Check here for more details about Win32_VideoController class.