Why ginger reacts with sparkling water?
According to this Wikipedia article:  


  Carbonated water (also known as club soda, soda water, sparkling water, seltzer water, or fizzy water) is water into which carbon dioxide gas under pressure has been dissolved. Some of these have additives, such as sodium chloride, sodium bicarbonate or similar, but seltzer water is almost always composed of water and carbon dioxide with no other additives. 


So the only possible candidates for a chemical reaction from the sparkling water are $\ce{CO2}$, and water itself. The other salts present at low levels would not have sufficient reactivity to produce the relatively high-energy results observed. And water can be ruled out as a reactant because ginger itself of course is a plant that contains water (or contained water previously if dried ginger was used). For the sake of thoroughness, I went to my kitchen and added tap water to dried, ground ginger and observed no effervescence.  

This leaves $\ce{CO2}$ as the only candidate for causing the observed reaction upon the addition of ginger to sparkling water. A chemical reaction can be ruled out from a couple perspectives. First, as $\ce{CO2}$ is a very stable, completely oxidized compound, ginger would have to contain some strong reducing agent for it to react. We know this is not the case as the ginger is produced and stored in an oxidizing environment (our atmosphere of $\pu{21\%}$ oxygen). The atmosphere also contains on the order of $\pu{0.04\%}$ $\ce{CO2}$, which is less than that found in sparkling water but would still have quenched any $\ce{CO2}$ reactive component, albeit in slower less dramatic fashion.  

At this point we've determined the effervescence must be a result of the $\ce{CO2}$ in the sparkling water, but we've eliminated the possibility of a chemical reaction. Because the carbonation process leaves the sparkling water supersaturated in $\ce{CO2}$, the only thing preventing the $\ce{CO2}$ from bursting out all at once is the lack of sites for $\ce{CO2}$ bubbles to nucleate. And this is what the ginger provides, particularly if it were in a ground, high-surface area form, but even in the case of raw ginger slices there are many more surface sites available than a glass container.  

Bottom line, TL/DR: There is no chemical reaction, rather the ginger just provided a relatively high surface area for the rapid formation of $\ce{CO2}$ bubbles from the $\ce{CO2}$ supersaturated sparkling water.