I think you need to say what you mean by "conscious" and by "choice." You've asserted that choice is a conscious process, but that's almost certainly not true, and studies like this prove it. That doesn't mean that you don't have free will, though. It just means that you don't make decisions at a conscious level. At a conscious level you may go over the inputs to the decision (or you may not), but the decision is then taken by unconscious mental processes acting either on the inputs that you considered, or not, depending on whether you put your attention on the decision.
The problem with the argument "there is free will" versus "there is not free will" is that the terms are poorly defined. By "free will" do you mean non-determinism? This is the traditional meaning, but the two aren't opposites. You can't have free will if the universe is deterministic, but the universe is apparently probabilistic, yet that doesn't mean that you necessarily have free will. If the outcome of your decisions is non-deterministic, but there is no conscious agent directing it, is that free will? What if it's an unconscious agent whose behavior is affected by conscious intentions? Where do the conscious intentions come from?
This is a really hard problem. Tests like the one in this study do not determine whether or not there is free will, but it's easy to grab attention by claiming that they do, and this is why such claims are made. Either that, or it's just inevitable.