Computer cabinets are made in a standard specification to match almost all motherboard configurations. These kind of standardised PC cabinets are called as ATX cabinets. All motherboards are compatible to every ATX cabinets on market. But SMPS position may change as some cases keep SMPS at bottom while some keep them on top. It's not a big deal as you can keep your SMPS upside down as well.
So in your case the answer is Yes. You can use your old pc case for your new gaming PC. Best wishes for your new gaming rig.