OK,Dave.Let the other readers take all this in,and do as they will.I've posted my responses:
1) An employment contract sets out the nature of the duties required and the amount of pay and benefits etc. This part of the contract is usually set out quite clearly and precisely. Once those duties have been performed, the employee's free time is his own and the exclusivity clause would not apply. The employer has no rights to control his employee's free time nor to dictate what he shall/shall not do in his free time as long as the employee does not break the law of the land. Agreed!But if you take this matter up with him to eliminate such illegal clauses before signing the contract,which would be the honest thing to do,my guess is that the job offer will be withdrawn!
2) If an employer fires an employee for working for someone else after the employee has fulfilled his contractual working duties, the employer may be liable for legal action for breach of contract himself, as he can prove no loss, expense, or other detriment due to the exclusivity clause being 'breached' The purpose of that clause is to reasonably protect the employer against loss and expense that might be caused if an employee performs work for someone else at times when he should be physically working for his employer. Thus when he has fulfilled his employer's duties there is no likelihood of this happening.But it could be argued that an employee can take on a second job to the detriment of his first job,in the sense that he is overworked doing the two jobs,and is therefore underperforming in his 'main' job!So he could be rightly(or wrongly) fired for that reason!

3) There is no question of 'cheating' as the purpose of the contract is not to restrict the employee's rights but to form the basis of an agreement as to what each party shall do for the other. I repeat - Once the employee has fulfilled his working duties his free time is his to do with as he pleases.But it's dishonest to sign a contract including a clause(or clauses) you'll subsequently disobey on purpose!
4) Thousands of foreign teachers in China perform teaching jobs for other schools 'on the side' without depriving their employer of anything at all. Thus the employer cannot claim he is being cheated simply because his employee uses his own spare time to earn extra cash. What is the employer losing by this? What cost is he being put to by this? All his costs (salary, accommodation, fares, utilities etc) are costed into the pay and benefits package offered to the employee and after he has performed his duties he has fulfilled his contract. So what exactly is the employer being cheated of? Answer - nothing! He is being cheated by those foreign teachers who are working on the side,possibly for second employers who have no right to hire foreign teachers in the first place,such teachers using the accommodation provided free by the initial employer and their Z visas arranged by said employer to benefit other Chinese employers who have paid and done nothing to hire them in the first place.And you have failed to mention that those teachers working on the side are taking away employment opportunities that would perhaps otherwise be offered to would-be foreign teachers who can't get jobs!

5) How many foreign teachers do you hear of being caught by the PSB? How many do you hear of being fired for working elsewhere? In all my years in China I can count such examples on the fingers of just one hand. Working elsewhere is not policed nor enforced to any significant degree, for it is something of a grey area.But if you're working anywhere in China without a Z visa,you're breaking the law,be it for one or more employers!(I haven't heard of FT's being caught teaching on the side because I choose to teach in backwaters,where there are few job opportunities anyway!)
6) You say (quite rightly) that my honesty or lack thereof is none of your business - but does the same comment apply to the honesty or lack thereof of all other foreign teachers - if so, why are you writing all your verbage at all? For if what I do is none of your business, neither is what they do and thus you shoot yourself in the foot for jumping in where you readily admit you have no business to be.Of course,the same comment applies!I was only stating that I regard it as dishonest,and likely your initial employer will regard it as so too,if he becomes aware of it.And don't forget that in China,employers sometimes look for other ways to fire employees whom they know have disobeyed the clauses of their contracts re working on the side.

Finally,what do you do if you're caught teaching on the side by your initial employer two months before the end of your contract and he withholds air fare reimbursement and other benefits?Take him to court and win your case before your residence permit has expired?On foreign soil,be prepared for anything,even the worst outcome!