On the one hand, what the chart does't show is that the location quotient for natural resources and mining in Harris County is 2.78, meaning that it is almost three times more reliant on the sector as the rest of the country. Despite this, however, only about five percent of jobs in Harris County are in that sector. The county in which Houston sits is actually very well diversified, with 75 percent of its jobs being in the service sector. Put another way, over the past several years, Harris County has been creating more total jobs every two years as there are jobs in the entire natural resources and mining sector.
NRS jobs do pay well, which means that any reductions in these jobs would have a multiplier effect (but we are generally terrible at estimating regional multipliers). But clearly something is happening in Houston that makes it attractive to employers that have nothing to do with the energy sector. My suspicion is that inexpensive housing is one of those things.
I could be completely wrong about this, but it seems to me that the decline in oil prices will more likely bring slower growth--as opposed to recession--to Harris County.