The chief software engineer in a company is going to have the best balance of an understanding of the needs of the business and building reliable/excellent technical solutions to difficult problems.
IMHO some of their traits are:
- Favouring time-to-market over elegance of solution. This doesn't mean producing inelegant solutions, just that a solution that delivers earlier will be more profitable in the long-run.
- An aversion to ground-up re-writes as they've learned the cost through experience.
- Ability to give accurate work breakdown structures to the business with realistic cost estimates and schedules.
- Can deliver on (3).
- Commands respect with the rest of the engineers in terms of being someone who gets results.
- Shying away from shiny new technology until it is well understood and has continuing industry/community support.
Some of these traits develop over time; some of them may get a kick-start by doing a secondary degree. Personally, I think that time spent in the subject of software engineering would equally help towards these goals. Remember that some of the big names in the industry do not even have degrees.
Fundamentally, getting promoted up to this role is going to require all other engineers to leave/die, or saying and doing all the right things such that those with the power to promote you to this position do so.