An engine system is disclosed. The engine system may have an engine with a plurality of cylinders, and at least one injector associated with each of the plurality of cylinders and configured to inject liquid fuel and gaseous fuel. The engine system may also have a turbocharger driven by exhaust from the plurality of cylinders to pressurize a flow of air directed into the plurality of cylinders, and a valve disposed inline with the turbocharger and configured to selectively increase an exhaust backpressure. The engine system may further have a controller configured to selectively cause movement of the valve toward a flow-restricting position only when the at least one injector is injecting gaseous fuel.