Ice from Greenland and Canada is melting and flowing into the northern North Atlantic, slowing down the Gulf Stream. This is quite well known in the climate community, which might be why the article did not explicitly say it.

Of course, all of that northern ice melting and turning into water must have nothing to do with how water moves in oceans.

This is most likely caused by changes in ocean temperatures. Those changes are part of climate change.

Global weather is an extremely complex system. Any change will have knock-on effects on the rest of the system. If the changes are big enough, you start seeing big effects like this.

I'm not sure what your example is meant to show. An ocean-scale current isn't something you can walk up to and mess with. But burning forests is certainly a contributor to climate change, which would be one of the causative factors in ocean warming and currents changing.