Therefore, (a) the data sorted by (year and weekofyear) pair, and (b) the data sorted by (week_start_date) have different order.
Can I assumes that the data sorted by (week_start_date) have right order?

Yes, the problem is that drivendata decided to use the year of the date that week_start_date represents. The example is 1993-01-01 the answer is 1993. However, the week number originates from the week based year, which - depending on the representation, e.g., ISO 8601, the week based year is 1992. See https://en.wikipedia.org/wiki/ISO_week_date for more details.