Hamiltonian Path Zero Knowledge Proof using Commitments to a Series of Edges
This does seem to be zero knowledge; as you say, you don't actually commit to the adjacency list. Rather, you commit to a series of edges, in random order.

Regarding the question: First, your assumption is that $n^2$ commitments, each to a single bit, is more expensive than $|E|$ commitments, each to $2\log n$ bits (to encode two numbers for the edge). This is a reasonable assumption for many commitment schemes but not necessarily for all. (Of course, it is very reasonable for sparse graphs.)

However, the main thing here is that the proof of Hamiltonicity is a theoretical proof of feasibility. Improving the concrete cost in this way is not of great interest. In any case, the protocol is unlikely to be used (applying a Karp reduction and then using Hamiltonicity will kill you in almost all cases).