What is the meaning to close Google apps source code According to the recent news, google apps are closed source and one cannot use it after forking android.

But, as I understand, I can fork Android, create my own OS and then install Gapps manually.

If the users can do it manually, theoretically anyone with any device can use Gapps, than what is the advantage of closing the source if it does not prevent Google from creating other Android alternatives, e.g Cyanogenmod?

EDIT: I am quite aware of the advantages of having closed/open source. The question is that Google wants to get rid of competitors and prevent Android fragmentation. People can fork Android and one day become major OS provider. OF course, forking android without google services has very little value for users and it is extremely difficult to write such services from scratch. So, Google tries to keep its leadership in Android market by closing its service.

But, if one can fork android, customize it, than use Google services (even if installed manually), than this does not help Google at all in reaching its goal, i.e. prevent competitors and Android fragmentation.The Google services still can be very easily used and everyone can have its own alternate Android. So, what is the point to close the services?

Besides this, again, what is the meaning to have Google approved devices?I can  manufacture devices and use their services without having the approval.
Technically, you are not allowed to "install Gapps manually" unless your phone already comes with them pre-installed.  The Google Apps package (that includes Google Play Services, Play Store, and several other apps) is Google's intellectual property, and nobody is allowed to distribute it, except for Google's certified partners that have passed CTS.

For example, CyanogenMod ROM does not include, host, or distribute the Gapps package. Instead, they have scripts built into their tools that back up Gapps that are already installed on your handset prior to  installation/upgrade, and restore them afterwards.  Any other ROMs and maintainers who do host Gapps packages are doing so illegally, and are infringing on Google's copyright.  For the most part, Google chooses to not enforce their copyright against small-time guys, but will not hesitate to unleash their army of lawyers when they deem is necessary.

To answer your question, Google's services are essential for their grip on Android's ecosystem. Only the big guys like Amazon or Samsung can afford to completely steer clear of Google's services with their own offerings. For example, not having access to Play Store on an Android handset is a huge drawback for a smaller manufacturer like HTC, Huawei, Motorola, etc., since the alternatives are usually lacking in both numbers, as well as (perceived) security.  Google uses this as both a carrot and a stick.