Javascript does not allow you to set the seed for the default PRNG. So for our purposes it's essentially non-deterministic. You need to use a custom library if you want to be able to specify your seed.
Continuing the nitpicking: "JavaScript" isn't actually what prevents setting the seed, you're talking about a common implementation detail of specific JavaScript runtimes (Mozilla’s documentation says their seed can't be changed, for instance). A runtime developer could, as Googlebot apparently does, seed the prng with a constant value. You could also use some user-provided constant as the seed. All three are compliant with the letter of the spec.
Bottom line: the PRNG is, as all PRNGs are, deterministic. The user-facing math.random API using the underlying PRNG may or may not be. Those are distinct things.
From the spec's description of math.random with regard to random or pseudo-random:
"...using an implementation‑
dependent algorithm or strategy."