Is it permissible to pay a sum of money to individuals who control the distribution of delivery requests in order to increase one's chances of obtaining requests and improving income, and is this considered usury (riba)?

There is no usury (riba) in paying money for a delivery service, and there is no harm in paying money to the application owner. However, if the person taking the money is an oppressor who is exploiting the application and is not its owner, then the default rule is that it is forbidden to pay money to him, except in cases of necessity to repel injustice or to prevent paying more than what was given, and the sin falls upon the one taking the money.