In the debate linked to in the question Michael Fallon asserts the following:
Over time, with the carbon price floor and a strengthening emissions
trading scheme, the economics of coal generation will deteriorate
further compared with gas.
And a bit later on:
I have also considered the argument that the amendment would provide
greater certainty to investors looking to build the new gas plant that
we all agree will be needed. [...] We already face a significant
investment challenge with an estimated 16 GW of new gas plant, and
about 45 GW in total of all forms of generating capacity, needed over
the decade from 2015 to 2024.
I take it from this that the amendment is intended to increase the generation of electricity from natural gas. If the demand for natural gas increased, this could certainly increase the incentive to invest in fracking in turn.