Ubuntu 10.04 64 bits
I have tested with build 2051 and libgio-cil 2.22.2-2 but this problem still occurs! :-(
"unable to load libgio, single instance support disabled"

$ ldd sublime_text
    linux-vdso.so.1 =>  (0x00007fff81f01000)
    libgtk-x11-2.0.so.0 => /usr/lib/libgtk-x11-2.0.so.0 (0x00007f771a22b000)
    libgdk-x11-2.0.so.0 => /usr/lib/libgdk-x11-2.0.so.0 (0x00007f7719f7e000)
    libatk-1.0.so.0 => /usr/lib/libatk-1.0.so.0 (0x00007f7719d5c000)
    libgio-2.0.so.0 => /usr/lib/libgio-2.0.so.0 (0x00007f7719a4b000)
    libpangoft2-1.0.so.0 => /usr/lib/libpangoft2-1.0.so.0 (0x00007f7719821000)
    libpangocairo-1.0.so.0 => /usr/lib/libpangocairo-1.0.so.0 (0x00007f7719613000)
    libgdk_pixbuf-2.0.so.0 => /usr/lib/libgdk_pixbuf-2.0.so.0 (0x00007f77193f7000)
    libcairo.so.2 => /usr/lib/libcairo.so.2 (0x00007f7719174000)
    libpng12.so.0 => /lib/libpng12.so.0 (0x00007f7718f4c000)
    libpango-1.0.so.0 => /usr/lib/libpango-1.0.so.0 (0x00007f7718d02000)
    libfreetype.so.6 => /usr/lib/libfreetype.so.6 (0x00007f7718a7c000)
    libfontconfig.so.1 => /usr/lib/libfontconfig.so.1 (0x00007f7718846000)
    libgobject-2.0.so.0 => /usr/lib/libgobject-2.0.so.0 (0x00007f77185f7000)
    libgmodule-2.0.so.0 => /usr/lib/libgmodule-2.0.so.0 (0x00007f77183f3000)
    libgthread-2.0.so.0 => /usr/lib/libgthread-2.0.so.0 (0x00007f77181ed000)
    librt.so.1 => /lib/librt.so.1 (0x00007f7717fe5000)
    libglib-2.0.so.0 => /lib/libglib-2.0.so.0 (0x00007f7717d06000)
    libpthread.so.0 => /lib/libpthread.so.0 (0x00007f7717ae8000)
    libdl.so.2 => /lib/libdl.so.2 (0x00007f77178e4000)
    libutil.so.1 => /lib/libutil.so.1 (0x00007f77176e1000)
    libm.so.6 => /lib/libm.so.6 (0x00007f771745d000)
    libX11.so.6 => /usr/lib/libX11.so.6 (0x00007f7717127000)
    libstdc++.so.6 => /usr/lib/libstdc++.so.6 (0x00007f7716e13000)
    libgcc_s.so.1 => /lib/libgcc_s.so.1 (0x00007f7716bfb000)
    libc.so.6 => /lib/libc.so.6 (0x00007f7716878000)
    libXext.so.6 => /usr/lib/libXext.so.6 (0x00007f7716666000)
    libXrender.so.1 => /usr/lib/libXrender.so.1 (0x00007f771645b000)
    libXinerama.so.1 => /usr/lib/libXinerama.so.1 (0x00007f7716258000)
    libXi.so.6 => /usr/lib/libXi.so.6 (0x00007f7716048000)
    libXrandr.so.2 => /usr/lib/libXrandr.so.2 (0x00007f7715e3e000)
    libXcursor.so.1 => /usr/lib/libXcursor.so.1 (0x00007f7715c34000)
    libXcomposite.so.1 => /usr/lib/libXcomposite.so.1 (0x00007f7715a31000)
    libXdamage.so.1 => /usr/lib/libXdamage.so.1 (0x00007f771582d000)
    libXfixes.so.3 => /usr/lib/libXfixes.so.3 (0x00007f7715627000)
    libz.so.1 => /lib/libz.so.1 (0x00007f7715410000)
    libpcre.so.3 => /lib/libpcre.so.3 (0x00007f77151e1000)
    libresolv.so.2 => /lib/libresolv.so.2 (0x00007f7714fc8000)
    libselinux.so.1 => /lib/libselinux.so.1 (0x00007f7714da9000)
    libpixman-1.so.0 => /usr/lib/libpixman-1.so.0 (0x00007f7714b50000)
    libdirectfb-1.2.so.0 => /usr/lib/libdirectfb-1.2.so.0 (0x00007f77148cc000)
    libfusion-1.2.so.0 => /usr/lib/libfusion-1.2.so.0 (0x00007f77146c2000)
    libdirect-1.2.so.0 => /usr/lib/libdirect-1.2.so.0 (0x00007f77144a9000)
    libxcb-render-util.so.0 => /usr/lib/libxcb-render-util.so.0 (0x00007f77142a4000)
    libxcb-render.so.0 => /usr/lib/libxcb-render.so.0 (0x00007f771409b000)
    libxcb.so.1 => /usr/lib/libxcb.so.1 (0x00007f7713e7f000)
    libexpat.so.1 => /lib/libexpat.so.1 (0x00007f7713c55000)
    /lib64/ld-linux-x86-64.so.2 (0x00007f771a86d000)
    libXau.so.6 => /usr/lib/libXau.so.6 (0x00007f7713a50000)
    libXdmcp.so.6 => /usr/lib/libXdmcp.so.6 (0x00007f771384a000)

I think this is a bug.

What version of libgio?
I have tried with libgio-cil 2.22.2 and libgio-fam 2.22.0 but it doesn't work.

It lacks of documentation.