You cant see equally in every direction. You assume you can because your eye is round, but each eye has part of its vision blocked by your facial features such as nose and brow. Unless your eye is on a stalk or you are grotesquely deformed, these areas are permanently vignetting your sight. The lateral side of your vision has the greatest periphery, the superior part the least. The medio-lateral axis has greater coverage than the supero-inferior axis (in laymans terms you can see more side to side than you can up and down).
You would think this would be noticeable but it isnt very because your eyes are used to it throughout your life. You also are almost unable to see colour at the edge of your vision but your brain fills it in for you without you realising.
And here I thought Thork was the resident expert on semantic derails.
The point of the original comment about line of sight had nothing to do with eye/face anatomy and the relative extent of your peripheral vision in various directions. I think we can all fairly agree that the video in question was shot using some sort of camera, which presumably has a symmetrical lens system for capturing images and a symmetrical boundary restricting outside light.
In such a device, the field of vision is indeed circular (or approximately so). If a camera can only see (hypothetically) objects 40 yards directly in front, then barring any major defects we can take this to be the radius of its field of vision. Said another way: if a camera pointed along the x-axis can see objects up to 40 yards away along that axis, then it will not be able to see objects 40 yards along the x-axis and 1 yard along the y-axis; it will, however, be able to see objects within the circle defined by x^2 + y^2 = 1600 (within the left/right bounds of its vision of course).
The original comment about line of line of sight was meant (I think) to imply that for objects receding into infinity we will observe a circular shape over a large enough area, presumably because we can only see to a certain distance. Thus, for a flat Earth that extends infinitely along its plane, any observer sufficiently high up will note a circular boundary to the portion of Earth that they can see.
If you really want to find flaw with the argument, ask instead about the reasons which might limit the distance that we can see. Without obstruction, light will travel into infinity. In this case, observing blackness beyond a certain radius indicates that either there is nothing in that direction at all to emit/reflect light, or that there is something that is obstructing the light.
If it were the first case, then there would not even be a question of the shape of our line of sight. Since the poster (Hazbollah, I think?) made the comment, we must therefore assume that he believes something is obstructing light from traveling after a long enough distance.
The only thing possible to obstruct light in this case is the atmosphere (a reasonable candidate, to be sure). The problem with this, however, is that such an observation of a very regularly-shaped circular section would require an extremely homogenous chunk of atmosphere between the observer and the horizon. Without this homogeneity, different amounts of light will be obstructed over different areas, and the horizon that we see here would not be very regularly shaped.
It is well known that the atmosphere is far from homogenous. It may contain a fairly regular mix of gases, but it varies greatly in density, moisture content, temperature, etc. (hence, weather happens). All of these things would affect the transmission of light through the medium. The clouds alone in this video are enough to demonstrate that no such homogeneity is being observed.
So the question becomes: If you expect your observations from limited field of vision to imitate a circle, then you must also expect the limiting factors to be regular along the field; when no such regularity exists, what else could be an explanation for the observed circularity?