No, it's worse at flat management companies like Valve. Since you don't have anyone in charge, and everybody works on what they want, there is no objective measure of whether or not you're doing well. Everything comes down to politics, from bonuses, to who gets laid off during downsizing, being very good at your job isn't enough. That's how it's been at the flat management company I worked at, and how it seems everyone who's worked at one describes it.
Yeah, I think the complaint was that Valve is/was theoretically flat, in that people could self-manage, but in practice, it had an implicit hierarchy that was obscured by the officially "flat" structure (which, let's be honest, was always kind of a lie, because I guarantee you there's someone there who can fire other people, which means it's not actually flat). And an implicit hierarchy means that there's no way to say "I had these goals and objectively achieved them"; you aren't making your case to a defined supervisor, you're making a case to the informal supervisor. That'll almost always wind up with favoritism without any potential escape.
Some of these problems exist in any company, but at least in a standard hierarchy, if your boss is sabotaging you or ignoring you, there are routes you can take (go to their boss, go to HR) to (imperfectly) route around that. In a flat structure, you're grasping at ghosts - after all, no one's your manager, so it shouldn't matter if one person has it out for you, but of course, if they're politically entrenched, it absolutely does matter. And there's no one in the company to complain to, because the company's official position is "this is impossible, we're a flat company", and your complaints are minimized if you complain externally, through some combination of "sour grapes" + "but it's a flat system!".
Honestly, it's a great trick on management's part - everybody has the responsibilities of management, but no one is an official manager, and there's an easy playbook to run on anyone who complains.
Any "objective measure" that a regular company uses is mostly a way for management to pose and bluster about what they actually want. Corporations are fundamentally all the same.