There is a free version of Highcharts, but it primarily pertains to personal (non-commercial) use. The most obvious answer to your first question is: because it's the law. Highcharts licenses their software for certain entities to use, so without obtaining the necessary license, you would be in violation of the applicable law. (I'm not a lawyer, so don't take this as legal advice.)
As for your second question, if you used their software without the correct license, they would probably only find out if someone informed them. The license requires neither a key nor activation, so there's no real registering of your usage of it.
I would strongly recommend purchasing the necessary license, rather than trying to use the software illegally for free. The "High-five License" is a very affordable option, but being a startup, if you contact their sales team, they may be able to work with you on pricing.