It's an older Delta, which as you say, is not (and was never) used to supply the ISS.
Image source: Wired article on the Delta II
Delta II flew its last mission in 2018. (wikipedia)
I don't know if this is the footage used in the show, but one of the Delta missions, GPS-IIR-1, suffered a really spectacular failure of a solid rocket booster not long after launch, resulting in the most amazing shower of flaming solid propellant that I'm aware of, melting cars in the parking lot, etc.
Some joker dubbed music over it, and the resolution is low, but here's a video of that.
Another video with some higher resolution footage (hat tip to DevSolar)