First, never take a seller's word for anything, as my experience has been that many sellers know little, if any, more about what they are selling than the buyer. I hate to say it, but the video is crap and does little to provide any identifying info. So, let's do a process of elimination here based on what it DOES show.
MaxxFarce engines did not debut until a bit later than 2002. So we can pretty much rule that one out. They are also painted black factory, unlike their tried-and-true predecessors, which are painted a very decidedly blue color that to some can appear blue-green. A 2002 is likely one of the E-designated HEUI variants of the DT466 or T444, aka the good old 7.3. I am not sure if the DT530 or DT408 were available in 2002.
Point blank, the T444(E) is a V-8, with the turbo mounted atop the intake manifold. The DT466(E) is an inline-6 with the turbo tucked to the right side. You don't get a good enough shot to even see the turbo, let alone where it is located.
Most, if not all Navistar engines should have their identifying info on a label somewhere on the engine, usually on the rocker cover. On a V-8 such as the T444, this will usually be the passenger side rocker cover, along with power ratings, etc.
Transmission ID is a little trickier, and while the pattern layout on the shifter can help in identifying the trans model, Allison installs a tag factory that will be on the right rear of the trans case (which for RE models will be toward the driver's side axle tube). This tag will have an unmistakable stamping of the trans model (AT545, MT643, 2000, MD3060 are the most common).
A 2002 is likely to have the 2000 or MD3060, I believe the AT545 and MT643 were only available as reman units by then, no longer a factory offering in new vehicles. A 2000 will have a T-handle shifter with either
R N (D) D 2 1
R N D 4 2 1
The MD3060 will have a flush console with an LED display, and buttons for R, N, D and up / down. This transmission is actually a six-speed auto, but sixth gear is locked out for skoolies. There is info here about how to unlock it if equipped with this transmission.
As for the shifter helping to ID the trans model....
But remember, the only way to positively ID trans model is to crawl under and read the tag. For some, the shifter can only narrow it down to a choice of two.
I do see some things that are notably different from T444 engines I've seen. Factory A/C often has both compressors at the top of the engine. Not so here, this one's appear to be mounted top / bottom on the driver's side. Another interesting difference here is that the T444's oil dipstick is on the passenger side below the exhaust manifold, and I didn't catch it in the video. You can't really tell where the turbocharger is located, but the previous two clues indicate a DT466, as a previous poster said.
But photos or video of the engine and trans tags will be needed to be sure. For Navistars, an alternate method of verifying this info is to call a Navistar dealer with the CORRECT VIN. Even one character misread will foul any attempt to look it up.