I am not an expert but according to Wikipedia BSCCO is not suitable for high magnetic field strengths. In the video - which I only skimmed - the main point seems to be that they can now build vastly smaller fusion reactors because now super conductors supporting higher fields strengths are available and the energy density of a fusion reactor scales with the fifth power of the magnetic field strength. They also specifically mention rare earths which does not match BSCCO which were, last but not least, also discovered in the late 1980s.
The biggest question in my mind about the ARC proposal is how well these new superconductors stand up to radiation. This is a concern for ITER as well, which uses more traditional superconductors. The ARC team is looking into it, but I'm going to remain unenthusiastic about ARC until they've really proven out the concept.
Around 33 minutes into the presentation he does address radiation briefly, noting that it's favorable because most of the issues relate to the ceramic insulators in traditional SC magnets. In their design, the steel structural component of the tape serves as the insulator; they just wind up the SC tape and the current travels along that 1um SC layer.
More generally, the demountable coils suggests that designs could be made where the magnets are replaceable with some degree of economy.
