The classical frequentist interpretation of a confidence interval doesn't require invoking Fisherian hypothesis-testing. It's simply an interval estimate for a population parameter rather than a point estimate, which is semantics close to what he means here. A 95% confidence interval is an interval estimate with 95% coverage probability for the true population parameter, which in the frequentist sense means that it includes the true population parameter in 95% of long-run experiment repetitions. (One can get different kinds of frequentist coverage with a prediction or a tolerance interval, which vary what's being covered and what's being repeated.)