Depending on what you need done, you are (or are not) requested a health examination at an approved entity.  In the specific case of the residence permit, to get a new one, or to renew it, you are required to get a good health certificate.  If some foreigners are getting away without it, should not brag much about it.

Legally you do have to get one done every year to prove you are not bringing some illness or whatever with you into the workplace.  If the other people didn't need one then that's just a loop hole your company is exploiting.  Have you tried asking your boss why this is so?  

Maybe your nationality has something to do with it.

It's like everything else in China, there is the black and white law and then a huge grey area in between. Legally, the medical should be carried out every year and some provinces do. But other provinces don't bother. Sometimes the requirement even varies within a province.

All kind of factors give rise to this. I am pretty sure in some provinces, the PSB take back handers from approved health check centres for ensuring the requirement is carried out. Then there is employer guanxi. And then just plain indifference. As long as you get the RP,just go along with whatever the local requirement happens to be. It is not your concern. 

To renew visa for half year u don't need physical exams, one and more year usually need it. If u change the type of visa (from F to Z or others) u also need it