It's not a humblebrag in terms of dollars. The idea being conveyed is that he (she?) should be unfire-able due to excellent performance (that's the brag), but that at-will employment negates the unfire-ability. I'm expressing doubt that 120% bonus is actually evidence he's such a great employee.

I think you may be missing how the bonus system works at many companies. 100% is defined as the maximum contractual bonus for consistently excellent performance but there is a separate discretionary maximum for exceptional cases beyond the contracted bonus. This discretionary bonus cap is often on the order of 50% higher than the contractual bonus cap. It is for when the maximum bonus is insufficient to reflect individual performance. A 120% bonus typically denotes a discretionary bonus beyond the contracted maximum, which almost always implies you are doing amazing work beyond the scope of your role.

Details vary by company of course but the tiny percentage of people who earned >100% bonuses at companies I've worked at were exceptional performers.

If the cap is an extra 50%, why did this guy only get 20% extra? In fact, he had 8 chances to get the actual max, and failed every time.

That's not the point. The point is performance reviews are poorly correlated with actual job performance, they aren't designed to measure job performance.

Would you hire someone knowing nothing other than they got 120% bonus at their previous job?