I don't understand the question. Proposal: if you sell it, you must recycle it. Question: how would an online shop do this? Obvious answer: by accepting the to-be-recycled product, just like an offline store? Whether they do the actual recycling themselves or contract a third party is up to them of course, but that's the same with any local kiosk that happens to sell batteries.
(Not saying I think it's a good or bad proposal btw. It sounds good, but there's going to be uncountable cases where the original retailer does not exist anymore, or you don't know where you bought something, or you've moved, etc. Whether to just accept that and consider it a net win, or if a deposit system would work better, no idea. I just don't see the problem with online stores having to accept goods they sold for recycling.)
(Not saying I think it's a good or bad proposal btw. It sounds good, but there's going to be uncountable cases where the original retailer does not exist anymore, or you don't know where you bought something, or you've moved, etc. Whether to just accept that and consider it a net win, or if a deposit system would work better, no idea. I just don't see the problem with online stores having to accept goods they sold for recycling.)