I just checked and shell access is an extra. Im not sure where the q2 folder should go. in public.html or the root? I have full ftp access. The host is www.justhost.com if that tells you anything.
Usually a web host like that won't offer the ability to run a persistent server process like Q2. I didn't see game servers mentioned on their list of services. Do you have a reason to expect to be able to run a Q2 server on this host?