Do you need to ground a gas dryer with a separate ground wire? Electric wire has 3-wire small socket.

Just use a regular 3 prong power cord. If you only have a 2 prong outlet, you need to install a properly grounded 3 prong outlet.

The gas line will also provide another ground. I would use a ground fault outlet since clothes are wet. You will be well protected then. Just make sure and clean the dryer once a year because it can still burn the house down if too dirty.