No, plastic cutting boards do not dull knives faster than other cutting boards. In fact, the type of plastic used, high-density polypropylene, has similar properties to soft wood, and it is gentle on your knives. Be sure to check the feel of the plastic, though. Very hard plastic can dull your knives. Sometimes plastic cutting boards might say “safe for professional knives” so you know you can use them without damage.
However, I must say that I do not believe that plastic is a good choice for cutting boards. Wood has the same ideal texture, all while being more attractive, and not harboring bacteria or putting microplastics into your food. Plastic might be cheap and convenient, but those ugly scratches are porous and can habor bacteria that may not be killed in the dishwasher. A recent study found that plastic harbors this bacteria much longer and more often than wood, and it is not the most hygenic choice as once previously thought. Besides, wood cutting boards just look better.
Although plastic cutting boards are generally safe for professional knives, I would recommend soft wood cutting boards over plastic because they have less of the other drawbacks.
