Ferhad, I have spent some time researching this problem and as far as I can ascertain, the links are not available via the Youtube V3 API. However, like you, I'm not convinced that I've explored every option; it's just not clear in the available documentation.
I just did this test: visit the About page of a YouTube channel, e.g. https://www.youtube.com/user/Gap/about, you'll that there is section called "Links" with many URLs. I believe you'll find this on many YouTube channels. I looked at both the YouTube and Google+ APIs (thinking the links might be coming from a linked G+ account), I cannot find a way to retrieve those links via the API.
I tried using "Channels: list" with these parameters:
- part=auditDetails,brandingSettings,contentDetails,contentOwnerDetails,id,invideoPromotion,snippet,statistics,status,topicDetails
- id=UCKdDR4GsvrA3yeDhMykoiPQ
- fields=etag,eventId,items,kind,nextPageToken,pageInfo,prevPageToken,tokenPagination,visitorId
The links were nowhere in the data.
Since there was a linked Google+ account, I tried looking over there, thinking they might be shared between the two platforms. I tried using "People: get" with these parameters:
- userid=100521075388356747359
- fields=aboutMe,ageRange,birthday,braggingRights,circledByCount,cover,currentLocation,displayName,domain,emails,etag,gender,id,image,isPlusUser,kind,language,name,nickname,objectType,occupation,organizations,placesLived,plusOneCount,relationshipStatus,skills,tagline,url,urls,verified
The links weren't there. The next area of exploration would be to see if they are only available via OAuth2, but again, it's not evident from the documentation.
Sorry that this is only a partial answer but some times it's hard to prove a negative.