Well I think it all depends on how the cafe staff communicated with the mother when it happened. If they simply handed her paper towels and looked on saying nothing, I can understand the mother being upset. She might have felt they were disapproving as well.
Hindsight is a wonderful thing. The the article does not say if the staff on duty actually told the mother their health and safety concerns. After all, this was a specifically child friendly cafe and the mother had paid to be there - ie paid for their service. If she had accidently spilt a coffee why would she expect to clean it up unaided?
I can certainy see why the staff would not want to be dealing directly with vomit, can see the health and safety reasons, but children do puke up and really as this cafe specifically welcomes children the staff should have been more helpfulIMO and equipped with plastic gloves etc so they were protected. Yes, the mother should have helped clean up but the staff should have been doing something as well.
Incidently, a similar thing happended to me when my son was a toddler. We were at a theme farm on a wet, rainy day. We were in a small playbarn when my son suddently made a dive for the open door, let down his trousers and had a wee into a rainy puddle near the entrance. I rushed over but I was too late. A young male helper saw what happened, stormed off and a few minutes later handed me a mop with a bucket of disinfectant and told me to clean up outside as it was disgusting. I refused point blank, asked to see the manager and complained long and hard. I got an apology.