For that, you can use a regex:
(get-content c:\users\abcusernamehere\desktop\findusermachines.txt) -replace '.+\\(.+?)\.txt:.+','$1'
ABC64ZXZ
ABC63BZB
ABC61ZSF
ABC62ETB
ABC60BBB
There's really no point in using Select-String to search for the lines that have the server names if they all have one. Just use Get-Content, and run the -replace operator against all the lines.