Energy demand from fossil fuels and renewables increases when you decrease transport energy efficiency, for example in this scenario.

If you decrease the energy efficiency of transport, more energy is needed to produce the same amount of work. Since oil is the dominant energy source for transport, demand for oil in this scenario increases more than demand for other energy sources. This greater demand for oil increases its cost by more than it increases the cost of these other energy sources. The higher cost of oil then causes the market to shift to other sources of energy, and the proportion of energy from non-oil sources increases slightly relative to the baseline scenario. 

The percent of transport that is electrified also increases slightly for this same reason, as that electricity is generated in large part by natural gas, coal, and renewables. When you multiply those higher proportions of non-oil energy sources by the greater transport energy demand, this results in increased demand for gas, coal, and electricity.

The depletion effect is also at work here. The supply of oil is subject to resource constraints, and greater demand leads to encountering those constraints sooner than for other fossil fuels, and thus making oil more expensive.