I really think people are too overrating binance, I know it's a popular exchange and could bring fame to project but little to nothing I've seen people speak about binance while discussing about doge, it's mostly because of elon that it pumps like this and elon's influence transcends the exchange itself
It is true that everyone is giving Binance more credits than they deserve and Dogecoin is a popular coin in the market and there are several crypto based gambling sites that accepted Doge and it was a popular coin for small time gamblers and the price started its rally when Elon Musk started but if you think back he was shilling the coin for a long time and now when he shilled when the entire market was rallying it had a really big impact.