I think traditional ramen is not a vegan dish, not least going by the definition of it on Merriam Webster. The dictionary defines it as noodles served in veggies and meat. However, I have also seen internet definitions that categorize the noodles as vegan products.
 
In any case, it is not the dictionary definition or online definition that matters the most here. What matters more is the specific ingredients in the product. You can make vegan ramen noodles at home after going through the plant-based recipe required for it. However, when shopping for ramen noodles online or offline, just keep an eye on the ingredients. What if there is any non-vegan ingredient in the specific product that you are thinking about buying? Just do not take any chances. A good thing is that there are several vegan ramen noodles available in the market.