Each steam account can only run one game from its library at a time, no matter how many PCs it is installed on. I can play the same games on both, but not at the same time. Just log into steam on that PC with your account. Yes, you can run your steam games account on any PC. Can you play the same steam game on 2 computers at the same time? Then enable the sharing feature via Settings > Family, (or in Big Picture mode, Settings > Family Library Sharing,) where you’ll also authorize specific computers and users to share. To enable Family Library Sharing, first be sure you have Steam Guard security enabled via Steam > Settings > Account in the Steam Client. How do you share games on Steam and play them together?
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