If the facts that went into that spot are right (which is unlikely due to inconsistencies) there's some issues.
Based on the orbital speed given at 3:17 (5 miles per second), they'll be in upper low earth orbit, about 500 miles. With a little fudge for air resistance (because I'm not going to bother estimating the friction coefficient for what I guess a rod is shaped like) that puts the impact speed of a body released from that height right at mach 10 (11250 feet per second). But wait, there's more. They did not seem to calculate any impact speed from the orbital velocity. Depending on how much of a retroorbital impulse they give the rod, it will still start with most of that 18000 feet per second (about 5 miles per second) lateral speed. That won't make any direct difference in how long it takes to reach the ground, but it sure will make a difference in how much energy it has at impact with stationary land. That's why a meteor impact can be so destructive - it's not just the height it falls from, it's how fast it's going before it starts falling to earth.
Also, while that orbit of 500 miles is definitely in space, by any definition, it is not outside of the upper atmosphere. It will experience atmospheric drag, and without reboost burns it will fall to earth in three to five years. That's far from the "indefinite" loiter time advertised in the video.
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