Shouldn't deltaTime be defined as the 1 over the time interval between two frames?

I tried to consider it like this:

Suppose an object moves 3 meters between one frame and the next, and it takes 2 secs. If you multiply them directly like in the reference example, it gives us 3 meters/ frame * 2 secs /frame = 6 meters * sec / frame^2, whereas what actually occurs is it moves 3 meters in 2 seconds, that is 3/2 = 1.5 meters/second.

Also, why is it that in the example, 10 meters/frame retained its magnitude to 10 meters/second?

The script example is correct. Time.deltaTime is definitely a time, and is the time between this frame and the last frame. So, if you were rendering at 100fps, then deltaTime would be 0.01s. In the example the object is moving at 10m/s. It’s not accelerating, just has constant velocity. So, if you multiply deltaTime (a time) by a velocity (in metres per second) you get a distance in metres, which is how far the object moved in that time.

I didn’t fully understand your math, but possibly you’re making things more complicated than it needs to be.

distance, d = 3 meters
time, t = 2 seconds
deltaTime, x ( the time need for 1 frame to show )

Your first equation is wrong to begin with. Let’s do this calculation to see why(based on your first equation)

Velocity = 3 meters/ frame * 2 secs /frame

Let frame be 1 
// I don't care what frame is right now, deltaTime, 
// or number of frame per second, it doesn't matter


Velocity = 3 meters/ 1 * 2 secs /1
         = 6 meter * 1 second

What does 6 meter * 1 second means? It is meaningless, it is definitely not velocity ( meter per second ), nor can it mean anything else.

Further Inspection

When you move 3 meters in 2 seconds, your velocity, V is

V = d/t
V = 3 / 2
  = 1.5 meter per seconds

When you said d/x (3/frame), this is not related to the original question at all, you are saying that

distance travelled per delta time

So, you are now talking about the speed required to travel 3 meter per 1 frame

If we are running 25 fps, deltaTime = 1sec/25frame = 0.04 seconds
d/X = 3 meter / 0.04 seconds
    = 75 meter per seconds

Your second part is 2 sec/frame, which is t/x, which translate to

2 seconds divides by time required to finish 1 frame

which will become, total number of frame in 2 seconds

If we are running 25 fps, deltaTime = 1sec/25frame = 0.04 seconds
t/X = 2 seconds / 0.04 seconds
    = 50 frames