How are you closing steam?
clicking the X button.
clicking "X" or " _" button, steam is minimized
Yes, it does the same for me. KDE too.
It's an old bug, with relation to the no taskbar icon in KDE (and others) but now in KDE have a properly taskbar icon for steam, but it doesn't close to taskbar, it's only minimize.
How some users said here https://github.com/ValveSoftware/steam-for-linux/issues/1025 there is a workaround with launching steam with STEAM_FRAME_FORCE_CLOSE=1 steam but we expect a proper solution.
In addition, when you click (once or many times you do) on the steam taskbar icon it doesn't do nothing (the proper behaivour is to show steam, like in windows), and the taskbar icon menu that pop ups with secondary button are a little laggy.
All this stuff and the problem with window chats in KDE https://github.com/ValveSoftware/steam-for-linux/issues/266 are the two reasons because i don't use many often Steam in Linux
The close-is-minimize is deliberate behavior, as described in the bugs Lukas mentions.
The problems with the taskbar menu in KDE are outside of Steam, again as discussed in the bugs above.
when I close steam this don't minimize at the tray icon in KDE 4.10.
I'm using Kubuntu 13.10 updated