I believe will get Part 3 or a new TLOU game, just not any time soon. This is what Neil had to say at the end of the documentary for Part 2.
He has a concept, an idea for a third game that continues and expands upon the themes of the first two games but that's about all the official information we have regarding a Part 3. I don't believe this new interview with him confirms Part 3 is cancelled, anymore than the video above "confirms" Part 3 is happening.
We should also keep in mind Neil isn't exactly known for being truthful in interviews, he has lied multiple times about TLOU since the first game, and he even said at one point that we should not expect to see a Part 2, so I'd take anything he says with a huge grain of salt.
Besides, even if Naughty Dog have forgoed any plans for Part 3, I doubt Sony and HBO (or Max) want the franchise to die. I bet we are likely to see spin-off games and TV shows from other Sony game studios and HBO, there's just too much money to be made with TLOU and after the blunder that's been this current generation I'm sure Sony will not pass up on what would be easy money for them.