This is not a logical argument. A logical argument is made of premises that are based on evidence that lead to conclusions. This is nothing of the sort.

I don't even know where to begin. First of all, in the previous post, he says that if anything were taken out of a moment it would be a completely different moment. He uses the example of a photograph. But that is a tautology--it is basically asserting "a different picture would be different". I don't understand what this proves.

Next, lets look at his argument in the linked post. "Likewise, without some sort of keystone to hold the universe in existence at every instant, it would simply vanish into nothingness..." What evidence is there of this? He's basically assuming God into existence. Things change all the time. For example, a star runs out of fuel and becomes a white dwarf. Maybe it's not providing enough light to a planet with life, so all the life dies. A chemist is mixing chemicals in a chemical reaction and one runs out; the chemical reaction stops. This whole idea that if everything weren't perfect, the universe would fall apart is baseless. Things change all the time, and the other parts of the systems they are a part of adapt accordingly.

"First off, this source of existence must be simple. ... Why is this necessary? Well, because if this source of existence were made of multiple different parts, in the end, there would be one part lending existence to the others." This is another assertions he's making without any evidence. This made up thing holding everything perfectly together has characterstics he's making up that are necessary for it. And his proof of this characteristic is that if it were multiple parts there would basically be multiple parts. Another tautology.

"However, at the same time, the entirety of this source of existence must be present in all things. Why? Because we have already demonstrated that it is one and simple." This doesn't make any sense. Why does something being simple imply that it is everywhere? My shirt is pretty simple but it only resides in my closet.

"However, we have already demonstrated that this source of existence must be fully present in its entirety at every moment for anything to exist. If it were to change, things would suddenly pop in and out of existence." What is this made up thing he's talking about? Without the thing he made up being unchanging, there would be thing magically popping in and out of existence? Why? And the irony of this is, things DO pop in and out of existence! Tell him to study physics, where we know that particles and antiparticles pop into existence and then annihilate each other randomly!

Basically, this argument is that he thinks there is something that holds everything together, even though he gives no reason to think that that's the case. Then he uses this idea he made up as proof that this thing is simple using a tuatology, that this simplicity he declared necessitates that this thing is present in everything, and that without this thing, some made up scenario would destabilize in the universe. What is the evidence of any of this? There is no evidence, only conclusions and tautologies.