Great question! If the water is rich in positive hydrogen ions (H+). then yes it IS acidic. But in this case, we’re talking about neutral hydrogen gas, which is two hydrogen atoms tied together.
It can be confusing to hear “hydrogen water” because we usually think of hydrogen (meaning the hydrogen ion, H+) as acidic, and that is basically the definition of pH. The p stands for potential or power, meaning a mathematical exponent (in this case a logarithmic function), and the H stands for the hydrogen ion, which is just a proton and no electron. So pH literally means the logarithmic concentration of the hydrogen ion.