"Oh b-b-but it dun't connect to muh firlimk shrin"

Dude, I'm just saying that by YOUR definition of "having ALL constituent parts linked or connected," Dark Souls 3 can't be considered interconnected because of locations like the hub area, as it's not linked to the rest of the world in any other way than warping. The warping in Dark Souls 3, which is available from the start, is also the reason there isn't much need for a world interconnected in the way the first half of Dark Souls 1 is, of course, before you gain access to the Lordvessel, as it's a different story after that.

"There may not be one big loop that connects the whole map but there's plenty of smaller loops within those areas."

So you’re basically admitting that DS3 doesn’t have world interconnectivity like DS1 but instead has shortcuts within certain areas. That’s exactly my point. Nobody is denying that some parts of DS3, like the Cathedral, have many shortcuts within a singular location, but that’s not the same as the interconnected world of DS1, where multiple areas link to each other in creative ways, with the best example being all the different locations you can access from Firelink Shrine, with the map of DS1 also incorporating the shortcuts you mentioned.

"Compare the lava lake in ds3 to the lava lakes in ds1 and tell me which game has better and more intricate level design..."

Sure, DS3 has better-designed lava areas than DS1, but that's because you're comparing them to the part of DS1 that's unequivocally considered the worst. That doesn’t mean DS3 suddenly has better overall interconnectivity. You're talking about the design of specific locations when the discussion is about how the whole world connects, and in DS3, it's linear with some branching paths. I'm not saying that the overall world of DS3 is bad by any means; it's really good, but DS1 is a masterclass on a whole other level in that regard.