As a manager, you can tell if an engineer is happy with their work if they are comfortable with giving higher-ups constructive feedback about issues at hand directly. As an engineer, you can tell if a manager is actively working for you if you see at least some action performed as a response to your feedback. When both things happen, management might see an increase in reported problems during development, but they'll also see an increase in resolutions, instead of seeing fewer but critical issues that go unresolved.
Despite the title, the advice in this article is, I think, much more widely applicable than mere video game development. You should probably read it.
(Mere? Video games involve artists, musicians, UX, storytellers, and above all live and die on the strength of their QA teams. Nothing mere about it.)
There are useful war stories about financial mismanagement, fraud, management issues, and a short tale of a company that turned itself around by listening to the employees.