Yes, it's definitely considered a wallet. But not a very safe one. Cryptocurency Exchange also have security measures but is not advisable to store a large amount of Crytocurrencies. Hackers are tirelessly working to steal BTC's in an Exchange. Convenience is one of the common reasons why people are always storing their money in an Exchange. Also in real life, most people are not storing their money in bank because it also has the possibilities to be robbed, more likely in an exchange which is Digital