I am an engineer that manufactures viral vector based drugs, so I've got some perspective here. Gates is right, IP is not the concern.
Having worked for large pharma companies and with contract manufacturers (CMOs), even in the US and Europe many CMOs are just straight up incompetent. See the whole Emergent fiasco with 15 million doses ruined as evidence. CMOs are okay for making more standard sorts of biologic (ie antibodies), but often struggle with more novel projects. While viral vectors are considered to be more established tech than mRNA, it's still a really new technology for the industry, and the technology is still rapidly evolving. I'd expect that even most US/European CMOs would have some hiccups trying to make viral vectors.
Having a country like India make their own vaccines is a completely different story. India just doesn't have enough engineers that know viral vector manufacturing to execute on something like this. I've worked with Indian biologic labs before, and suffice it to say that my experience did not give me much confidence that India has the knowledge to build vector manufacturing capabilities from the ground-up. This is doubly true if the innovators themselves are not directly overseeing manufacturing. For instance, my understanding is that J&J is basically running that Emergent plant right now, but I doubt that sort of arrangement would occur for a failing Indian CMO.
Best option in my opinion is to provide incentives to these companies to expand production based on existing capacity. Merck acting as a CMO to produce the J&J vaccine is actually quite historic, in that Merck is a direct competitor to J&J as a vaccine manufacturer. More collaborations like that, using existing capacity at established pharma companies and CMOs, is in my opinion our best option for scaling up vaccine manufacturing.
EDIT 1: There is also a talent shortage right now. I've noticed that lately I've been getting tons of attention from recruiters, presumably because there aren't enough experienced engineers/scientists to support scale up of vaccine manufacturing.
EDIT 2: I also want to highlight that even US/EU CMOs would struggle to make a drug without support from the innovator. The US government has set up the "biosimilar" concept as a pathway to introduce competition for biologic drugs with expired patents. However, making a biosimilar is actually quite difficult, due to the inherent variability in biologic systems. For a biosimilar, it's not enough that your drug is safe and efficacious; it has to have the exact same safety and efficacy as the innovator. Without having the innovator cell line, it takes months or even years of work for competitors to engineer their own cell lines to replicate the performance of the innovator cell lines. Now, you could always just force the innovator to share their cell lines, but that puts you in the realm of appropriating actual property as opposed to intellectual property.