To quote Evelyn Waugh "Up to a point, Lord Copper." Which is a polite way of saying no, or at least not exactly. In the '60s, there were extra charges for the Aquarium and the Reptile House (and after they knocked that down, for the Tropical House) and of course for the Waterbus. At the moment there is an extra charge for the monorail, which I agree is a funfair element, although I'm not sure whether the free boat rides in Islands count as such. SMR is right to mention face-painting and much more merchandising too.*
There are more play areas than there were originally, but this is a sign of increasing visitor numbers and also of social change. At the start of the 1960s, the public car park was outside the entrance, it is now the staff car park outside the staff entrance. Most visitors arrived by public transport, and during the last half hour of their visits they regularly looked at their watches to make sure they didn't miss their buses and trains home. Now there are not only more visitors, but most of them arrive by car and as the zoo is much larger, visits last longer and there is more demand for refreshments and places for visitors to relax and for children to play. Look at old films of Chester or other zoos, things were very different in those days.
Zoos have always had to strike a balance between the demands of the animals and of the visitors. The pressures on commercial zoos are obvious, but not-for-profit zoos only have a little more leeway: collections owned by Merlin or Parques Reunidos have to offer what their visitors want, consequently Chester and the other collections owned by charitable trusts can hardly offer less, although they do not need to offer exactly the same things. As always, the question is - where do you draw the line?
* 2 gerunds in the same phrase