As a professional programmer, this is not abusing the code in any way. A glitch is defined as "a sudden, usually temporary, malfunction or irregularity of equipment." That's not what's happening here. Nothing is malfunctioning. Everything is working exactly as designed. The case is that the fence was not designed high enough to prevent a player from using the as-designed jump function from jumping into the next area. Either as a result of fence height as designed, or placement of burlap sacks (I would argue for the latter in a development meeting).

In the video he is literally just using the jump button to jump. Watch that video I linked to see an actual glitch that abuses how the code works. In the video the zip is executed when Sonic is stuck in a wall somehow and presses left or right. Since collision detection is designed to stop you from going into a wall in the first place, pushing left against a wall makes the game push you back to the right so you aren't embedded in it. As a result, when you're already inside a wall holding left or right causes you to travel in the opposite direction much faster than you can attain by normal play. It's a glitch because 1) the code normally kills you when you are "inside" walls and this is prevented 2) you exceed the cap for travel speed 3) your position is incremented instead of dying or being placed above the wall. Megaman has something similar where the vertical axis of the game is wrapped, so you can grab ladder on the bottom of the screen by jumping off the top. Ocarina of Time has this where you can write memory addresses by using bottles and teleport to near the end of the game from near the beginning of the game.

If jumping over that fence is a glitch then including the jump command in the game in any capacity is a glitch.

It might have be unintended, but it's not a glitch. An art asset that is too short isn't a glitch.