Yes, I agree, video understandable, the idea of curvature of our space-time is old as the world. I don't understand why passing near a massive object a ray of light has exactly such curvature as in the picture - deviates from the mass. By the way, it completely contradicts the behavior of objects in the video you provide.
About the mass.
Curvature is good, but it's only a way to talk about it.
I cannot but confirm that these questions are better known to the creator of our world, if he himself has not forgotten what he did.
But the photon beam itself - it has a mass, and completely independent of the so-called curvature of space-time. That is why the heated gas in a closed measuring system - has its own weight, which increases with increasing temperature. Because as the temperature increases - there is an increase in the flow of photons of infrared radiation in the closed system. A closed system is one in which the photons do not fly out, but are reflected and remain inside (Thermos).  Temperature rise - is an increase in the flow of photons, an increase in their number. That is why the mass of such a system, when heated, will increase.
I think a photon has a mass of motion...
The fact that time and space are one continuum is only a hypothesis.  That hypothesis has a lot of evidence. But the opposite hypothesis that time and space may sometimes be not in phase, not in such a single and indivisible continuum as we think, also has no evidence to disprove it.
An electromagnetic wave is also a continuum of electric and magnetic fields. But, in the absence of oscillations, an electric field can successfully exist without a magnetic one.  And there is no continuum! It's broken.
This indirectly confirms that the continuum also has its own time-space (a more correct definition than space-time, in my humble opinion) oscillations which we do not notice while we are inside this medium. Probably, this continuum can be as broken as any other. Nature is infinite and does not like the limitations of its manifestation.
An example in support of this view.
The theory of black hole existence. A place where gravity is enormous. Time increases (let us define that when time slows down in relation to our reference system, it means that time as a parameter of the length of events increases (!!!), and not vice versa, it is very important not to confuse and not to give in to the opinion of one's "common sense", science has often proved that it is "common sense" that is false), and space in these conditions decreases.
Let's check it out.
The rate at which any object falls under these conditions relative to us seems to be decreasing. The object is slowing down. That's because there's more time than we have. Let's see: velocity V is distance / time. That's right, only in this concept of time and space evaluation, speed V by its formula tends to zero relative to our reference system. The object will never fall to the surface of a black hole, it will seem to us that it has stopped. Yes, I know the surface of a black hole isn't, that's the way to talk.
On the other hand, if we fell to the center of the black hole and were alive, we would see our universe moving faster and faster and all the stars flying apart at increasing speed, our solar system dying, new ones forming... Here's the continuum, clap and it's gone.

It turns out that the places where there is no gravity are places where time flows as slowly as possible and space is enormous. That's why there's a constant of maximum speed in this environment - the speed of light in a vacuum, but now you have to add it immediately:
1) in the place with the least gravity;
2) and immediately add - for our reference system, which is also in the place with the smallest gravity.
Here is what is not in the formula for the speed of light - no relativity itself.
If we were in a place with strong gravity (in a black hole), the speed of the same light - would be for us completely different, larger, huge, any.

Old Einstein was right to say that speed is relative. He was right to say that no other object in our world can move faster than the speed of light. But he didn't agree that this is under the condition that the gravitational field in the place where light moves and where we observe and measure it from. 
After all, speed is the ratio of two components of the continuum time/space: and space (distance) / time (length of event) - both there, in the formula for speed. And both of these parameters are not constant in nature.

And there are suspicions that gravity not only curves space-time, to be more precise, in my terms, violates the conditions of their inviolable continuum, but is also a clear characteristic of our world and, therefore, when it changes - a passage to other worlds.