First, they did not seem to make a thermodynamic loss argument. They made that argument for vertical farming versus regular farming to argue that the inputs to regular farming are cheaper because they are not harvesting solar energy with extra steps. That is a perfectly cogent argument because the inputs are the same in both cases. You can not make the same argument for solar energy versus drilling costs without making the reader fill in a ridiculous number of gaps in the argument.
Even assuming they did obliquely try to make a thermodynamic loss argument, it is irrelevant. Thermodynamic efficiency is not really related to electricity costs except indirectly otherwise we would all be using ultra-expensive 30% efficiency solar panels instead of cheap as dirt 10-20% efficiency solar panels. It is a contributor, but the core question is price efficiency of the non-"drilled hydrocarbon" energy commodity.
The thesis is that non-subsidized solar energy-derived electricity will be cheap enough relative to hydrocarbon synthesis efficiency that it will be cheaper to synthesize than drilling it out of the ground (at current prices). There are many ways to reject that thesis, of which you present at least a few, but the comment I was responding to did not bring them up.
Given their other responses, they keep acting as if the thesis is: "We will make synthetic hydrocarbons that are 10x more expensive than harvested hydrocarbons, but we expect people to buy them anyways for reasons" which is obviously a strawman. The point of the discussion is entirely in whether it will be 10x more expensive, where one side claims it will be cost-competitive and the other side disagrees. To that end, here are some options including ones you brought up that at least provide potential counter-arguments for the actual point under contention:
1. Solar energy is actually non-viable, but subsidies make it, incorrectly, seem viable.
2. Solar energy will not continue to become cheaper exponentially and reach a low enough price.
3. Solar energy will become very cheap, but synthesis will be too cost-inefficient anyways.
4. Synthesis is cost-efficient on a per-unit basis, but requires capital intensive processes that only pay back if continuously active which solar can not provide.
5. Synthesis is only efficient at the margins right now. There is actually a lot of cheaply accessible hydrocarbons that can accept price reductions and still remain viable. All you will actually displace is a tiny edge of barely profitable hydrocarbons until there are even more significant cost reductions.
6. Solar energy cost reductions will also reduce hydrocarbon harvesting costs in a relative proportion that keeps harvesting viable.
7. They just suck at execution.
8. Something else.