According to the video, there were some things that the Colosseum had in common with our modern sports stadiums.

One example of this is the system that they used of tickets and seating.  The video says that people who came to the Colosseum had to have tickets and that the tickets were not just for admission to the building.  Instead, they tickets were for specific seats in specific sections of the stadium.  This is like our current stadiums.

A second example is the fact that there was actually some amount of indoor plumbing.  There were drinking fountains in the Colloseum.  The video also claims that there were enough bathrooms to take care of the audience when the Colosseum was full.

How does the Colosseum's size compare to other Roman structures?

The answer to this can be found at about 2 minutes in to the video that you have linked to.  Basically, the Colosseum was bigger (or at least taller) than any other building built in Ancient Rome.  We are not told how much taller it was than any other building.  We are also not told how its overall size (other than its height) compared to the other large buildings of Rome.

According to the video, the Colosseum eventually reached a height of about 160 feet.  This was possible because of the Romans' ability to use things like cranes to lift heavy stones.