cost effective

I'm not so sure. A used Thinkpad comes with everything you need, whereas a PS3 or PS4 also needs a screen and a controller at bare minimum. The Thinkpad also has access to a game library of (checks notes) almost every single game ever made excluding mainly AAA titles from the 2010s onward. The PS3/4 is only the better value proposition if you specifically want to play those kinds of games, or if you highly value plug-and-play ease of use.