The article brings up some good points. As the price of petroleum goes up because of dwindling supplies (oil gets harder to extract/refine as time goes on) and increased demands (China's and India's rising middle classes, among others), it also stimulates demand for petroleum alternatives including biofuels. Biofuel is a substitute of gasoline or diesel, so as the price of gas/diesel goes up, biofuel's demand increases as consumers shift away from gas/diesel looking for cheaper alternatives.
Because of these increased demands for corn, rapeseed, and other biofuel crops, their prices go up. When a farmer is weighing growing corn versus barley, if corn's price is increasing, it makes the most sense to grow corn. Since land is a finite resource, as the price of corn and biofuel crops go up, farmers will inevitably switch over to these crops since they will get more money out of it. For them to want to grow malting barley instead, they will only do so if their profit is greater than or similar to the alternative of growing biofuels. As barley production is traded for corn production, barley will become more scarce (reducing supply) and causing an increase in prices assuming demand for malting barley holds constant (people will probably still drink).
Translation: as oil prices go up, the price of malting barley will go up as barley becomes more scarce.