I'm confused. They imply a 3 day trip to mars is possible, but is that at the maximum speed photonic propulsion can deliver, or do they include the acceleration and deceleration times? As I understood it, photonic propulsion can deliver extreme speeds, but only at a minimal acceleration. That means that maximum speed is much faster, but accelerating to that speed takes immensely longer, and the same goes for deceleration. Maybe they've invented a new method I've not heard of with much higher acceleration, but that's not really mentioned in the video.
They actually seem to imply they plan to use the same tech as cyclotrons, which means essentially a huge rail gun (and that's not photonic propulsion BTW, it's magnetic). Again, the amount of propulsion is miniscule, but the top speed is high with that method. Yes, you can expel matter at near speed of light, but only in tiny amounts and using huge amounts of energy.
Yes, it may take 10 minutes to achieve 30% the speed of light....with single molecules or atoms.
There are MANY reasons why we can't do this at macro sizes. Just look at the size of a cyclotron needed to accelerate an atom to those relativistic speeds. Now think about sizing that up to accelerate enough matter to move a spaceship instead of a single atom and it's likely near the size of the entire planet. We won't be building a cyclotron that size ever, nor will we likely ever shrink the accelerators to a size where they can fit inside a spaceship to shoot trillions of atoms out like a light speed gun. They are just too big and use too much power. Maybe once fusion is perfected and miniaturization also perfected it could work for interstellar travel, but never for local space travel, the acceleration levels are just too small.
Also, it seems solar sails give the same or better acceleration to the same top speeds without the impossible technology....but they don't work too well for stopping except at other stars.

Constant 1G acceleration followed by constant 1 G deceleration gets you to Mars in about 50-75 hours, and you never get anywhere near relativistic velocity. It's just a matter of scalability. If you develop an engine that can accelerate a given mass at. 001g, and it's made light enough that most of that mass is payload, you just scale up with an array of 1000 of them and you're at 1G.

I don't know about much of the stuff you've brought up, but they were pretty clear that the 3 day travel time was for a 100 kg capsule. They said that a shuttle would take longer (a month I think). It seems likely that this is due to increased mass, meaning that acceleration and deceleration times are included.