Sorry but GOG connect only has certain games for a limited time. You can't just sync your entire library.

The only game currently on GOG Connect is Renowned Explorers, so unless you've got that one on Steam there isn't anything to get. The games are only offered for a limited time. I suggest you read the FAQ on this page. If there are any games on offer that you can claim, you can do so on that same page.

Edit: You can also check out the first post in this thread of mine, it lists some useful links as well as past offers.

I'll just copy-paste the relevant section from the forum FAQ:

What happened to GOG Connect?
- GOG Connect games are not available forever. After a set period of time, you can no longer redeem whatever games were being offered on your GOG account. The deadline should be mentioned in the news post which has indicated what GOG Connect games are available. If not, it is possible that the staff has not assigned a deadline yet. Contact support or a staff member and ask.
- If there are no games available, check to see whether the deadline on the games has passed. If so, there will be nothing available until the next offer. GOG Connect has not necessarily been abandoned. Sometimes there can be a few months in between offers.


In short, it's as Omega pointed out. GOG Connect is a promotional tool that lets you get whatever particular games GOG picks during a certain time period, you can't just transfer over everything you have.

Thanks all.