I recently installed CU9 to BizTalk 2010. Microsoft site (https://support.microsoft.com/en-us/kb/3136004) claims that all previously CU are included in latest CU.
BizTalk Server uses a cumulative update (CU) model for providing fixes and updates. Each cumulative update includes new updates in addition to all the updates that were included in previous cumulative updates
Now I have problem with deployment ("Error saving map. Stored procedure returned non-zero result." error message when you deploy the BizTalk Server 2010 applications in BizTalk Server 2010 Administration Console") supposed to be fixed in CU4.(https://support.microsoft.com/en-us/kb/2667310)
So do I need to install all CUs from 1 - latest (for BizTalk 2010) to be fully upgraded?
You do not need to install all of them, the latest is just fine. They are cumulative as is stated.
That being said: have you tried uninstalling the latest CU (CU9) and installing CU4 instead? I assume you had no CU's installed before?
Unfortunately, lately Microsofts track records in relation to BizTalk CU's is not something to be proud of... There were quite a few issues with CU's already. It is not unthinkable that some CU after CU4 reintroduced the issue.
Also: the specific issue you are mentioning is something that was supposedly being fixed in CU4. However, this is just one particular case that was solved. There are still other remaining cases which have not been fixed yet.