It really doesn't look that large in the video.  It's hard to perceive scale.
 
I flew half way around the world in an Antonov AN-124.  It was pretty large.
 
Edit:  The Stratolaunch is really only the largest plane when judged by only width.  I would say that the Antonov AN-225 is still the largest plane overall; based not only on its length, but on its sheer size, robustness, and massive fuselage.  The Stratolaunch is dainty in comparison.

https://www.aeronef.net/2013/03/stratolaunch-size-comparison-of.html
 
Meh
 
 
I have seen the AN-225 on the runway in Kabul.  It was impressive.

 
That central wing piece between the two fuselages must be incredibly strong - landing and turbulence would place huge stress on it, particularly with no rear support to spread the load and keep the two fuselages in sync (for lack of a better term).
 
 

Here we were waiting to clear customs in Italy.



Look at the size of that tow bar.

I also saw the Dreamlifter at Boeing field.



I also got to work in a Lockheed Martin facility where they tested projectiles and propellants. That was pretty cool.

The AN-225 is still the largest. This one just has a longer wingspan.

Technically, it's a Lifter, so once you get a space worthy craft secured to it for stratosphere launch, it would be a pretty massive object taking off. I would guess it has very high mass regardless, as it would need a lot of structural strength to handle the payloads it is designed for.