I agree that the regulation is worded inappropriately, and that methylphenidate is not an amphetamine. However, I would like to provide a more thorough answer than "rxlist.com says so". We'll have to borrow a few ideas from organic chemistry.
Amphetamine is a substance with a specific molecular structure, shown below (under the title "Adderall"), and an amphetamine is any of many substances with molecular structures based on that of amphetamine (examples in the second image). You can think of amphetamine as the parent structure of a class of substances which are called substituted amphetamines or simply amphetamines. For instance, if the group of atoms circled in blue on the methylphenidate structure was placed on the amphetamine structure, you would have a substituted amphetamine ("an amphetamine").
Methamphetamine, MDMA, ephedrine, methylephedrine and pseudoephedrine are also amphetamines in this sense. I've highlighted in green groups that are added to amphetamine to produce some of these amphetamines.
So, why isn't methylphenidate an amphetamine? The blue group doesn't make a difference, because adding it to amphetamine would just produce a substituted amphetamine. It is the group of atoms circled in red that matter. You see, amphetamine is a portmanteau of alpha-methylphenethylamine, which signifies that amphetamine is a phenethylamine molecule with a methyl group (CH3) in the alpha location, as depicted below. (Phenethylamines are an interesting class of molecules in their own right, including many drugs and neurotransmitters such as dopamine, norepinephrine and adrenaline.)
The group in the alpha position is crucial to our question. If the group at the alpha position is not CH3, then the molecule is not an amphetamine. In methylphenidate, the group in the alpha position (circled in red) is a chain of four carbon atoms (and their associated hydrogens) which may be represented as CH2-CH2-CH2-CH2 (and happens to connect to the N atom at the far end, though this doesn't matter for our purposes). Since methylphenidate has a 4-carbon chain in the alpha position of its molecular structure, it cannot be called an amphetamine, because as mentioned in the previous paragraph the am implies there is a 1-carbon (methyl) group in the alpha position.
Despite this, methylphenidate and amphetamine do have a lot in common. They both belong to the functional class of CNS stimulants, as the OP and the other answerer are aware. In addition, methylphenidate and amphetamine do both belong to a common structural class, which is the phenethylamine class. That is to say, both methylphenidate and amphetamine are (substituted) phenethylamines.
Therefore, one way in which the chess WADA policy could be reworded is:
Phenethylamine Stimulants - Ritalin or amphetamines such as
Adderall, ephedrine, pseudoephedrine or methylephedrine, when
exceeding the urine concentrations listed below.
Using the category phenethylamine stimulants would be scientifically correct and provide a useful contrast to the category of non-prohibited stimulants, i.e. caffeine.