If it replaces coal mining for power production, fracking reduces CO2 emissions, but that's not the whole story. Burning anything results in increased CO2 emissions, and methane leaks in fracked gas infrastructure result in CO2 equivalent emissions that erase the gains in reduced CO2 emissions compared to coal.
Engel's argument rests on two key assumptions which have turned out true in the case of the U.S., which leads the world in shale gas production:
Natural gas replaces coal as a source of electric power.
This is basically true. With an aging coal fleet, increasing natural gas-burning generation capacity, and falling power prices, several economists have looked at the direct effects on coal consumption. Numbers vary, but anywhere from 28% to 49% of the reduction in U.S. coal consumption is a direct result of the influx of cheap natural gas caused by the shale gas boom (see also here and here for more nuanced analyses). This means that a world with shale gas burns less coal than one without it.
Per kWh produced, coal-burning plants emit more CO2 than natural gas-burning plants. This is also true. Per unit of energy, coal produces more than twice as much CO2 as natural gas (source) when burned in a power plant.
But Engel ignores something that recent data is confirming more and more: leaks in natural gas production systems are chronically under-estimated and probably eliminate the GHG-reducing gains made by the shift from coal to natural gas.
This was documented in an article in Science published in 2018. The article, "Assessment of methane emissions from the U.S. oil and gas supply chain", is behind a paywall, but Phys.org has a good summary. Here's the most significant finding (emphasis added):
[R]esearchers found most of the emissions came from leaks, equipment malfunctions and other "abnormal" operating conditions. The climate impact of these leaks in 2015 was roughly the same as the climate impact of carbon dioxide emissions from all U.S. coal-fired power plants operating in 2015, they found.
Net generation from coal and natural gas were roughly equal in 2015, with natural gas increasing and coal decreasing since then.
The reason for this massive impact, and why leakage is such a concern, is that methane as a greenhouse gas is 34 times more potent than CO2 on a 100-year timescale. And that's just the leaks -- the natural gas still has to be burned, which will produced additional CO2 emissions.
Strictly speaking, if you're intent on digging things up and burning them and all you care about is CO2, then shale gas is better than coal. But it's still putting CO2 into the atmosphere, and if you factor in the global warming potential of leaked methane, it stops looking any better than coal.