The Saturn V sent three astronauts 240k miles to the Moon, yet a rocket only twice as powerful will propel 100 people 135million miles to Mars. Been a long time since HS Physics but those numbers seem dubious.
The video mentioned that he would temporarily park the space ship in a near earth orbit and then send up additional fuel for the trip to mars.
Reading between the lines of the article, the actual 100 person craft would not be boosted into orbit fully loaded for the trip to Mars, but sent up empty to be fueled and fitted before the pioneers arrived in orbit on successive launches for the journey. I think that sounds doable. That is where the tankers mentioned in the article come into play. The boost into orbit through our gravity well is the hardest part. The giant engines fired from orbit toward Mars is a piece of cake by comparison.
https://www.youtube.com/watch?v=uvR9A4aylc0
Before the ship departs Earth orbit, reusable tankers would top off its fuel supply, much of which would have been spent getting it into orbit.
Then it would coast to Mars at 63k mph, break (the video glosses over this step), enter Mars's thin atmosphere, and land. After disgorging its passengers and cargo, the ship would be refueled (assumes fuel produced on Mars) and blast off for the return to Earth.
For energy enroute, the ship deploys 200 kw worth of solar panels.
Seems likely, if the window is right, leaving Earth’s orbit to circle around and intercept Mars just takes a bit longer burn than leaving Earth’s orbit to go to the moon. The travel time is a lot longer too, however.