Here you are asking is web development a pre requirement to get into cloud computing then my answer is no. Because cloud computing offers wide career opportunities such as Big Data, Machine Learning, Network Engineer, Security analyst, and many more. None of these streams require you to know about web development.
So no worries you make a career in cloud computing without having knowledge of web development. If you are planning to learn this technology so nothing can be as best as Cloud Architect Masters Course offered by Intellipaat.
Before enrolling do check out this video on how Intellipaat helped Sonu babu Joseph in her career transitioning from Web development to Cloud computing -