Yeah, in my experience this is really what it's all about. Thinking out loud helps them assess how you reason through trade-offs, potential ideas you run through, edge cases you catch, at what stage you catch them and how you go about addressing them etc.
Thinking out-loud also prevents candidates from going completely off the rails. Maybe they missed an important detail or are solving a different problem than what the interviewer intended. These things happen, better to catch them early in the interview.
