Answer

1. It is hard to define this well. One can think of aspects in which electricity is actually more continuous than an ordinary fire is (the current is constantly operating by virtue of the initial voltage difference).
2. But in any case I do not agree with his innovation, regardless of that. The microscopic description of the process has nothing to do with Jewish law. Just as I am generally not fond of indirect-causation mechanisms, as I recall I once wrote about here, based on Rabbi Yitzhak Brand’s argument.
3. True, there are halakhic decisors who distinguished between cooking and smoking or salting, which were not prohibited when done by non-Jews—that is, they made formal distinctions. But as a matter of reasoning, it is hard to accept a distinction between fire and electricity when it comes to the rationale of the prohibition. And this is what Shevet HaLevi writes (8, 185) regarding microwave cooking, that it is genuinely different from cooking with fire. So cooking with electricity is really just like ordinary fire-cooking in our times. Would he then hold that on the Sabbath too it would be permitted in principle to cook with electricity, on a Torah level? Would that be cooking by indirect causation? Highly unlikely. By the same token, his ruling regarding Sabbath candles also seems very unlikely to me (there one even has the Nimukei Yosef regarding the ordinary lighting of a candle before the Sabbath, that under the rule “his fire is considered like his arrows,” it is regarded as though one is lighting at every moment throughout the Sabbath itself. Would electric light not be considered “his arrows” for this purpose?!).