I'm using an Ubuntu 14.04 and a Wine 1.6.2. I successfully installed and ran GTA III from it and it works, except that there is no audio. I changed the setting from "speaker" to "headphone"(what I use) and even tried changing the in-game hardware options. It should be noted that I have never used Wine before this so it would most probably be a problem regarding Wine.
Wine is notorious for having problems with Pulseaudio, Ubuntu's default sound server. As a result, it is necessary for you to switch to ALSA. To do that, follow the below instructions.
sudo apt-get autoremove pulseaudiofrom terminal
sudo apt-get install gnome-alsamixer
Done! You can find more information here.
Additionally, Wine 1.6.2 seems to be outdated. Since you are trying to run games, you probably want the latest version. To install it, follow the below steps.
sudo apt-add-repository ppa:ubuntu-wine/ppa
- When asked, hit Enter
sudo apt-get remove wine wine1.6
sudo apt-get install wine1.7
After that, you should be running the latest Wine.