Doesn't look like Google provided a print option in their iOS app. You can't even get to the share sheet.
Actually, I was surprised to find out you could print out instructions from Apple's Maps app, and that it actually does a decent job. Thanks for pointing that out, even if it's not what you were after.
So, I played around trying to get a print-out of Google Maps directions. This is what I tried, and how well/badly it worked.
First, I abandoned the app and went to Google Maps in Safari. A straight printout didn't work very well. All I got was the Map and distance. Even then the map failed to print completely a couple of times.
So I tried sending it to my app PDF Converter (by Readdle). I got the turn-by-turn instructions, but no map.
Sending it to the Evernote app and printing from there worked best as a single step. It printed both the map and directions, but like the earlier map-only results sometimes not all of the map printed.
My conclusion is that if I need to print driving directions from Google Maps I would:
1) Use Safari and go to Google Maps.
2) Take a screen shot of the map portion, with the map expanded to show the most detail, and print that.
3) Use PDF Converter and print the resulting PDF of the turn-by-turn directions.
Kind of complicated but it should give you everything you need, and look at least a little better than using all screen shots.