Usually this should be an easy task – provided you've got a custom recovery on your device. Turned out, it was not as easy in this special case, so I will list multiple options here. In combination, they finally lead to success – as one can see in the comments on the question itself.
Variant 1: Custom recovery
That's a one-liner: Put the GApps archive on your SDCard, boot into recovery, chose "Install update.zip from SDCard", and select the GApps archive. Done. After the next boot, Google Apps should be there.
Trouble in this case: No custom recovery. OK, next one.
Variant 2: Use ADB to side-load it
This variant was even figured by the OP himself. Requires ADB to be installed on your computer (see: Is there a minimal installation of ADB?), and your device setup (device drivers etc.) as well as connected via USB. For a detailed how-to, please see How to: use "adb sideload" on your Android device. Here, in short:
- place the GApps zip file in the directory where your ADB executable is
- Make sure you have USB debugging enabled in Settings → Development on your device
- Boot your device in recovery mode, and connect it to your PC
- On your device, use the volume up/down keys to select "apply update from ADB," then press power to select it
- On your computer, open a command prompt window and navigate to the directory from 1., then execute
adb sideload <zipfile> (replacing
<zipfile> with the name of your GApps file)
- When the installation is finished, select to "reboot" the device.
Done. Once the device finished booting, your Google Apps should be there.
Or not, as in our case. Services got installed, apps were missing. OK, let's trick the remains.
Variant #3: Doint it manually
- Install ES File Explorer on your device. This will help us a lot.
- Unpack the Gapps archive into an empty directory on your SDCard. Might be an optional step, as ES File Explorer can deal with ZIPs directly, but might make things easier
Launch ES File Explorer on your device. Tap the menu button, tap "Root-Explorer" (the text, not the switch next to it – though you must make sure that's switched to "On" as well). A popup should open, where you should find a "r/w" icon (second to last entry). Tap that. This should remount your
/system partition, so you can write to it.
Now use ES File Explorer to navigate to your (unpacked) GApps archive. Copy the
.apk files from
/system/apps/ on your device. Similarly, files from
data/apps/ should be copied to
/data/apps/. Now back to the menu, and re-mount your
/system partition read-only.
Now, the Google Apps should be there.
Still not? Bang. Variant 4: Get another device... or at least another ROM...