I just saw a solution was published a few months ago. So I was wrong. And I am happy about it because it is the way it should be: to look impossible while being actually possible.
I suspect this puzzle to be impossible.
It wouldn't be the first time. See https://www.youtube.com/watch?v=FZqYxmbjvKc.
Let's name the elements from left to right on your 1st picture: A: big heart, B: white string, C: black string, D: white string, E: stick, F: white string, G: small heart.
CDEFG form a chain. The ring cannot escape between these elements. It has to get off one of the ends. Similarily, AB form a small chain. Since the ring cannot go over A or G, it has to get thru the knot between B and C.
B cannot go over G and C cannot go over A. Therefore B cannot get off the chain CDEFG and C cannot get off AB, you cannot take one of the chains AB and CDEFG out of the ring without pulling the other chain into the ring. There will always be either AB or CDEFG going thru the ring. This makes it impossible to get the ring off both chains.
I might be wrong. I would be really interested if there is anybody who can confirm he has actually solved the puzzle or seen it solved. If so I would buy it straight away. But for time being I suspect this puzzle is not solvable.
PS: My argument isn't airtight. In the second picture in the question, you can see that if the stick were shorter, you could just pull the black rope over the end and the small heart. What happens is that CDEFG could separate from AB if C goes back over CDEFG. But that cannot happen because C cannot go over the stick E. Therefore AB and CDEFG still cannot separate. I guess this fixes it.