I do not think it's good that they make a contest out of finding the most bugs. While it is true that their job is to find bugs, their job is not "find the most bugs". Their goal isn't to find the most, their goal is to help improve the quality of the software. Rewarding them for finding more bugs is about the same as rewarding a programmer for writing the most lines of code, rather than the highest quality code.
Turning it into a game gives them an incentive to focus on finding many shallow bugs, rather than finding the most critical bugs. As you mention in your edit, this is exactly what is happening in your organization.
One could argue that any bug they find is fair game, and that all bugs need to be discovered. However, given that your team likely has limited resources, would you rather have a tester focus several hours or days probing deeply into your system trying to find really big bugs, or spend several hours or days skipping through the app looking for typographical errors and small errors in the alignment of objects on a page?
If the company really wants to make a game out of it, give the developers the power to add points to a bug. "stupid bugs" get negative points, hard to find bugs with well written reports get multiple points. This then moves the incentive from "find the most" to "be the best at doing your job". However, this isn't recommended either, because a programmer and QA analyst could work together to artificially pad their numbers.
Bottom line: don't make a game out of finding bugs. Find ways in your organization to reward good work and leave it at that. Gamification rewards people for reaching a goal. You don't want a QA analyst to have the goal of "find the most bugs", you want their goal to be "improve the quality of the software". Those two goals are not the same.