Listing Windows domain computers without Remote Server Administration Tools (RSAT)

You can always use the ADSI interfaces via PowerShell/.NET and the System.DirectoryServices namespace.

Here's a quick example using DirectorySearcher assuming you're running PowerShell as a standard domain user.

$searcher = New-Object DirectoryServices.DirectorySearcher
$searcher.Filter = '(objectclass=computer)'
$searcher.SearchRoot = 'LDAP://DC=example,DC=com'
$searcher.FindAll()

It's not as nice as working with the ActiveDirectory module in my opinion. But it's definitely doable and in some cases can be faster than the ActiveDirectory module.

You may also be able to pull just the ActiveDirectory module files out of another installation and add them to your personal profile rather than needing to install the entire RSAT package. If I recall correctly, it's one folder and about 5 MB worth of files.