Data Management Gateway can work with or without ExpressRoute. Without ER, Data Management Gateway needs to be deployed to on-premises machine, and it will build Relay channel to be called from Cloud to retrieve data from on-premises. With ER, gateway could be deployed to an Azure VM within a VNET to access your on-premises data stores.
The point is that ER is a channel to accelerate and secure your communication between Azure and on-premises. While Data Management Gateway is an agent to execute Activities you defined in Azure Data Factory, which may contains many pipelines/activities for business. Without gateway you may need to implement your own solution to move data between Azure and on-premises, even with ER enabled.
