"the 104-year-old Graflex 4×5 view camera"
"view cameras" are a subset of "large format cameras". I think he's using one of the Graflex Reflex large format *reflex* cameras.
A "view" camera is usually one where the photographer uses a ground glass at the film plane to view the image to capture - which requires composing/focusing/inserting film/shooting, not useful for subject in motion. It may use large format films or not (there are 6x9 cm view cameras - which is medium format).
For this reason press cameras (like the later Graflex SpeedGraphic) were fitted with an external viewfinder to be used quickly, but retained the focal plane ground glass - that made them less bulky than the early reflex models.
In reflex cameras, the ground glass is usually above the mirror which is lifted when shooting, so no need to switch between "view" and "shooting" mode manually.
Camera like the Graflex were common in sports because they had a focal plane shutter which could achieve faster speed than leaf ones available for the lenses of the time, albeit distorting the images of fast objects (i.e. the oval shaped wheels of cars).
Shooting a Falcon 9 launch with a view camera is feasible - it's a perfectly determined event - you know where it is, and what it does every second, so you can plan well in advance.
Just shutter speeds may be limited, and long telephotos too especially for very large formats (the larger the format, the longer the focal). And of course, the film must be replaced manually for each shot (unless using medium format roll film).
Then some vintage look may be given by the lens and film/paper used, regardless on what camera they are used in (basically it's just a light-sealed box able to move to focus the lens on film).
Some old lenses had designs with specific uncorrected (or only partially corrected) aberrations, which gave them very specific "looks" (now some like the Petzval and others are being re-made just for this). Same for film. and many B/W ones specifically developed to increase speed will also deliver the grainy look.