That method simply calls through to randn(Random.default_rng(), T, dims...).
It is the latter function that is not implemented for T == Int64. Hence the MethodError for randn(::Random.MersenneTwister, ...) (note the first argument, which is an RNG object).
This is a pretty common pattern: a generic higher-level wrapper calls through to a lower-level function that actually implements the computation. That way, if you want to implement randn for a new type T, you only need to implement the lower-level method and you get the higher-level methods for free (since they are type-generic). The downside of this approach is that, for unimplemented methods, the MethodError is thrown from the lower-level function rather than the function that the top-level user is calling.