It's because it is arbitration, and arbitration is a binding process. They aren't taking their case to 'court' in the way we'd think about it. They're taking it to an expert that will make a decision for them, but it's for civil/family issues (between the two parties) rather than criminal (where the crown brings the prosecution and would remain free to do so if it had the evidence of a crime). So rather than going in front of a judge to determine what happens in respect of residency of children, it would be in front of the arbitrator.
You don't need to be legally trained to be an arbitrator although a lot are - the reason arbitration is used (usually in the context of business) is because you want the judgement of someone that is an expert in the particular area (although in this case, it would be Sikh laws) or a retired legal professional with experience in the area possibly supported by an expert, and therefore understands the nuances of the practical issues, rather than a legal expert that may not understand those nuances.
It's a consensual process, so both parties would need to agree with it (but that doesn't mean much when one side can be pressured into it). Effectively, people would actively waive their right to pursue litigation in favour of a binding decision being made by someone that is an expert in their culture. If you went to 'Sikh court' over residency, and didn't like the decision, you wouldn't then be able to pursue litigation in the normal way simply because you didn't like the answer. That binding award is what you signed up for when you agreed to arbitrate.