Course gamification: rewards that aren't bonus marks?

One idea is to include some problems/tasks in the final exam related to those competencies. This might not be possible.

A student who achieved the highest level in that competency automatically gets full grade on that question, and doesn't have to solve it (thus getting extra time for the rest of the exam).

For levels 1 and 2 you can award free part marks, and the student gets either the free marks or his grade on the problem (whichever which is larger).

Added

Depending on how long/short it needs to be, something like below might work (or could be terrible):

Exam:

Part A (short questions testing the competency parts)

Question 1 (competency A): bla bla bla

Question 2 (competency B): bla bla bla

Question 3 (competency C): bla bla bla

Question 4 (competency D): bla bla bla

Part B Actual exam, Questions 5- ...

My answer is based on the following points:

1. In theory, if a student has achieved a competency at a certain skill they should be able to repeatedly demonstrate said skill.
2. Students at the same proficiency levels should received the same grade.
3. Your gamification approach exists to help them achieve mastery in competencies A, B, C and D. It is not the only way of doing so and it shouldn't matter how they get there, as long as they do get there.
4. Your extra activities are well thought and helpful for students to achieve mastery in competencies A, B, C and D.
5. Students can see value in achieving the course's competencies.

Given these assumptions, an alternative idea is to not give bonus marks at all, but instead make the exam (or other high stakes assessment activities) an opportunity for students to demonstrate their mastery of competencies A, B, C and D. The questions posed should relate to all the optional activities and you can even make some a little more complicated to gauge proficiency in higher skills levels.

For those who have joined the gamified part of the course the exam should look like just another activity they have already completed. We expect their performance to match their level of skill obtained in the gamified part and students should be able to self-assess their performance with reasonable precision.

For those who do not join the gamified part of the course the exam might be their first opportunity to demonstrate the competencies. They may or may not do well, as they might not have prepared themselves for the exam. It is their risk in doing so, as joining the gamified part would have made the exam much easier (or at least much more predictable).

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Note that points 3 and 4 are essential for this to work. If achieving the course's competencies is not seen by students as interesting/challenging/useful then the gamified part risks becoming just pointless homework. The same goes for the actual tasks done during homework: if they are not properly contextualized and connected with the course's competencies they might also become pointless homework.