Your system information

• Steam client version:
  Using Beta Client
  Build: Apr 29 2016 at 22:27:58
  Steam API: v017
  Steam package version: 1461972496
• Distribution (e.g. Ubuntu): Debian
• Opted into Steam client beta?: [Yes/No] Yes
• Have you checked for system updates?: [Yes/No] Yes

Please describe your issue in as much detail as possible:

Describe what you expected should happen and what did happen. Please link any large code pastes as a Github Gist

Steps for reproducing this issue:

1. Start steam with with a game a Desktop shortcut (e.g Dota 2.desktop)

[Desktop Entry]
Name=Dota 2
Comment=Play this game on Steam
Exec=steam steam://rungameid/570
Icon=steam_icon_570
Terminal=false
Type=Application
Categories=Game;

1. Close Game, click in Steam on "Steam"->"Change User..."
2. Log in with an other account.
3. After login steam instantly starts the game you started Steam the first time (in this example Dota 2)