No way to adda googel account to android phone.... HELP!!!!!

Hi, I bought an INNOS D9 android phone, with android 4.1.2.
I would like to sync the calendar app with my google calendar of my google account on PC, but when I go on the phone to settings>account>add account there is NO Google account type to select! Only Exchange, Mail or what's up types.
Please note that this phone does not have Google play store on it: it has an appmarket chinese only app that I do not use obviously; I downloaded the play store apk from the web and installed it, but it does not run ( the app closes immediately after being launched).
Then I installed the amazon appmarket app, which is working OK.
Also, at first startup the phone did not ask me to specify a google account, as I have read most phones do.
What I should do to be able to specify a google account and get goggle calendar sync in this case?
Thanks

Yes I do have a jellybean 4.1.2 phone, and no it's not straightforward that if it's android you must have google account type:
This happens if you have the Gapps or Google apps (not open source like android) installed, on top of android. Which is commonplace for western markets but not in China where the Innos D9 is sold. In fact, I do not even have Google Play store; I am using amazon app store instead.
However I have solved this in another way, installing the calDAV app which is actually an alternative way to sync almost any calendar to the web, including google calendars.
So I should say I am happy now....
Thanks anyway