so, it is proof of work, it's just not "a proof-of-work lottery"

Yes, in the strict sense of the meaning. In general, the comparison of VDFs (a cryptographic building block) and Bitcoin-style PoW (a consensus mechanism) is not that useful. However, using a VDF as part of a consensus mechanism (see e.g., Chia) does not introduce an energy overhead.

To demystify what a VDF is, consider the delay function (i.e., the majority of the work done to compute a VDF) used by the most prominent proposals:

Let N = p*q be a product of two large primes (so an RSA modulus) and assume that the primes p and q have been immediately thrown away/forgotten after initialization. Then, computing

f(x) = x^(2^T) mod N

is believed (dating back to a paper by Rivest, Shamir and Wagner in 1996) to take T sequential steps provided that T is large enough. For a large T, the only feasible approach seems to be repeated squaring modulo N. That is, compute y = x^2 mod N, y' = y^2 mod N, ... for T times.