Remember that if you host the game you need to open the ports for Steam in routers/firewalls.

This is from Steam own support page:

Steam Client
- UDP 27000 to 27015 inclusive (Game client traffic)
- UDP 27015 to 27030 inclusive (Typically Matchmaking and HLTV)
- TCP 27014 to 27050 inclusive (Steam downloads)
- UDP 27031 and 27036 (incoming, for In-Home Streaming)
- TCP 27036 and 27037 (incoming, for In-Home Streaming)
- UDP 4380