In my experience, it's ideal to have your optimization as close to the desired business results as possible. It sounds like in your case that's account creation of first game play. I consider that my default. That said, I've had two kinds of situations pull me away from the default.
The first is scale. If you're doing an ongoing campaign the default is fine, but short-burst campaigns may need a higher-funnel conversion like an install.
The second is incrementality. I've had situations where optimizing for the business result directly was cannibalizing organic conversions. But when we optimized to a discovery-related event, it wasn't. Examples of discovery related events might be searches in the site/app, or reads of deep informational pages.
So, default to what's closest to your business result unless scale or incrementality suggest otherwise.