I'll never agree with those explanations (which doesn't exist in Spanish).
The sentence is "no quiero/quisiera" [conveying different nuances] "que se rompa el récord" simply because "
no quiero que se rompe el récord" makes no sense in Spanish.
The reason is English indicative and Spanish indicative are quite different. When you use indicative in Spanish, the action expressed in the verb is being carried out. In Spanish you say "llueve" because it's indeed raining. You can't say "
puede que llueve" because it's not raining -it's almost that simple- so we have subjunctive to refer to actions that for some reason are not straightforwardly happening "puede que llueva" as with Spanish subjunctive it may rain or not.
If you tried to say "
no quiero que se rompe el récord" there would be two actions that are happening in that sentence: you want something and the record is broken, altogether. A native speaker would try to make sense of it by hearing "no quiero, que se rompe el récord" (I don't want to, because the record ends up broken). If you don't want the record
to broke, you have to do something exactly like adding "to" in front of the verb in English. In Spanish, subjuctive is handy to that and many other tasks, so by "no quiero que se rompa el récord" we understand that "you want", and the record is not breaking but you want it unbroken.