Please include information requested on https://github.com/ValveSoftware/steam-for-linux

Of course. I am sorry I did not supply the information right away.

How to reproduce:

• Install Ubuntu 12.10 64bit
• Use both, Intel "Ivy Bridge" CPU integrated graphics and dedicated nVidia graphics card (BIOS initializes integrated graphics first)
• Keep intel driver shipped with Ubuntu
• Add proprietary nvidia drivers by installing package nvidia-current (this usually breaks openGL rendering on the Intel screen due to libGL.so.1 mismatches). The package nvidia-current-updates and nVidia's own installer produce equal results.
• Configure X server for two separate screens, e.g. with supplied xorg.conf
• Run steam on Screen1 (the one with nvidia graphics card) by either specifying the DISPLAY environment variable or using an application launcher or a terminal located on Screen1.

Section "ServerLayout"
    Identifier     "X.org Configured"
    Screen      0  "Screen0" 0 0
    Screen      1  "Screen1" LeftOf "Screen0"
EndSection

Section "Module"
    Load  "glx"
EndSection

Section "Monitor"
    Identifier   "Monitor0"
    VendorName   "Monitor Vendor"
    ModelName    "Monitor Model"
EndSection

Section "Monitor"
    Identifier   "Monitor1"
    VendorName   "Monitor Vendor"
    ModelName    "Monitor Model"
EndSection

Section "Device"
    Identifier  "Card0"
    Driver      "intel"
    BusID       "PCI:0:2:0"
EndSection

Section "Device"
    Identifier  "Card1"
    Driver      "nvidia"
    BusID       "PCI:1:0:0"
EndSection

Section "Screen"
    Identifier "Screen0"
    Device     "Card0"
    Monitor    "Monitor0"
    SubSection "Display"
        Viewport   0 0
        Depth     24
    EndSubSection
EndSection

Section "Screen"
    Identifier "Screen1"
    Device     "Card1"
    Monitor    "Monitor1"
    SubSection "Display"
        Viewport   0 0
        Depth     24
    EndSubSection
EndSection

Swapping Card0 and Card1 in the Screen sections solves the issue.
Additional information: You may experience https://bugs.launchpad.net/ubuntu/+source/xorg-server/+bug/1068920 while reproducing.

Console output:

Relevant lines from TF2 start

SDL video target is 'x11'
Failed to create SDL window: Couldn't find matching GLX visual

Trine 2 fails silently (with a segfault)

System Information:

Processor Information:
    Vendor:  GenuineIntel
    Speed: 3201 Mhz
    4 logical processors
    4 physical processors
    HyperThreading:  Unsupported
    FCMOV:  Supported
    SSE2:  Supported
    SSE3:  Supported
    SSSE3:  Supported
    SSE4a:  Unsupported
    SSE41:  Supported
    SSE42:  Supported

Network Information:
    Network Speed:  

Operating System Version:
    Ubuntu 12.10 (64 bit)
    Kernel Name:  Linux
    Kernel Version:  3.5.0-21-generic
    X Server vendor:  The X.Org Foundation
    X Server release:  11300000

Video Card:
    Driver:  NVIDIA Corporation GeForce GTX 460/PCIe/SSE2

    Driver Version:  4.2.0 NVIDIA 304.64
    Desktop Color Depth: 24 bits per pixel
    Monitor Refresh Rate: 60 Hz
    VendorID:  0x10de
    DeviceID:  0xe22
    Number of Monitors:  1
    Number of Logical Video Cards:  2
    Primary Display Resolution:  1280 x 1024
    Desktop Resolution: 1280 x 1024
    Primary Display Size: 13,31" x 10,63"  (17,01" diag)
                                            33,8cm x 27,0cm  (43,2cm diag)
    Primary Bus: PCI Express 16x
    Primary VRAM: 1023 MB
    Supported MSAA Modes:  2x 4x 8x 16x 

Sound card:
    Audio device: Realtek ID 892

Memory:
    RAM:  7885 Mb

Miscellaneous:
    UI Language:  English
    LANG:  de_DE.UTF-8
    Microphone:  Not set
    Total Hard Disk Space Available:  693140 Mb
    Largest Free Hard Disk Block:  189063 Mb

Installed software:

Recent Failure Reports:

I know it's not likely to help, but upgrading to the experimental 310.x series of drivers may be of some benefit to you.

I'd suggest updating Mesa for your Intel chipset, but I've heard some bad stuff regarding Kubuntu and Mesa 9.

I had only problems installing the driver manually, so if you install via Jockey you'll be fine.
Installing drivers manually is bad practice, since those files won't be handled by the package manager and are almost guarenteed to lead to file conflicts when you switch back to using the package manager and don't do a clean removal first. Furthermore it wouldn't surprise me if you couldn't start into desktop anymore after a kernel update since the nvidia module is compiled against your current version of the linux headers at that time. So new kernel might not be compatible with the "old" module.

The latest driver is 313.09 btw.

Thank you for your comments. Indeed you point out a problem with my installation. I can tell you that the nvidia kernel module is properly registered to DKMS (so there should be no problems with kernel updates) and the links to the GL libraries are fine. Nevertheless the rendering system seems broken whenever nvidia is Screen1. Keep in mind whenever nvidia is configured on Screen0, it works perfectly. I was confident everything was fine because glxgears is running, but I just found out it's probably the only application which is working. I try to investigate further.
Issue can be regarded as invalid until further notice.

Closing at poster's suggestion that this is not a Steam bug.