Bare with me here because I am not an expert. I think what they're getting is the same as how gravity doesn't exist. Vsauce did a great video on that, but the general notion is that because space time is curved, objects traveling in streight lines will appear to be drawn closer to one another. "Gravity" isn't fundamental, warping spacetime is. Nothing changed but our understanding of it, which does matter for some more complicated areas.
I think this is similar. Just like gravity "doesn't exisit", it's just an emergent phenomenon: they're saying so is time. They're saying time isn't fundemental, except that it's an expected phenomenon that would arise from other factors, those factors being proposed to be some entanglement crap I have zero ability to talk about.
And I'm putting some words in their mouth with "time isn't fundemental". What they're really doing is proposing a new definition that better fits observed phenomenon/models.
And still, none of this explains why we still have daylights savings time.