Would MySQL highscores/leaderboards be sufficient to get a financial analyst job or would I need to make a standalone app which relies only on databases?
Depends on the job.
If the job is for a junior developer, or for someone who rarely works with database, or for a position where they are willing to help you learn, then maybe. But if it is for a job where they expect many years of experience and competency, probably not.
During an interview a good interviewer will ask questions that go deeper, and deeper, and deeper, until they figure out how much you really know.
Normally a technical interviewer will start simple, asking you for the code needed to retrieve a few values, how to insert some values, update, and delete. Then they'll ask harder questions, like some joins, some tabular computations like the best in a list, or code to help with pagination (display 1-10, 11-20, 21-29, ...), and similar. They'll dig deeper asking about indexes and maintaining indexes and using hints. They'll ask about security models. They'll ask about data correctness. They'll ask about isolation levels and concurrency tickets.
And they'll keep asking questions until they really know how much you know.
If you are looking for a job requiring 5+ years of database programming experience you should not expect to get the job if your exposure is writing a high score table one time.
But if they are looking for someone who has had a small amount of exposure and are willing to work with you because you know the rest, then you might be a great candidate.
Just don't lie, because they WILL discover it sooner or later. Lying is an effective way to either get passed over for the job if they catch you early, or fired from the job if they catch you later.