Your intuition is right. Here's how I would explain this phrase. The range of items that you will not be permitted to bring with you to the test center include wristwatches, cellphones, calculators and other similar objects. However, there are probably millions of other things a person can take with them when they go somewhere. It would be practically impossible to list every single one of them. So, here we give you a list of the items that you are specifically not allowed to have with you at the test center, but due to the impracticality of listing all possible items that you can't bring with you, the list is not limited to the ones directly specified.
Here's another example:
He has done scientific work in many different fields of science including but not limited to physics, mathematics and biology.
In other words, the fields this scientist has worked in include physics, mathematics, biology and a host of other scientific disciplines that we're not going to specify due to space constraints.