I am a regular into CAG which, as you would probably expect, now has white "Xs" painted on the closed runway/taxyway in question, along with cones/lighting across at various intervals.
Regulars (presumably like this crew) will also know that for the last year prior to 9th April) all ATC approach and landing clearances have had to be read back ackowledging the side step onto Runway 32 Right, and this has been reinforced by ATC to the extent that it becomes routine...and hence susceptible to confirmation bias or however you would wish to refer to it. I am not using this as an excuse for what happened, but I can see why the potential for the mix up is there. I can confirm that the ongoing works have been pretty regularly updated in Jeppesen and Notams (legible or not) and most of us seem to have been aware of the new implementation date for the new runway which has been put back several times already.
I too have received landing clearances from Approach Control. The reason seems to be that a "late landing clearance" by the tower is considered to be anything up to 5 miles out when, in my book, a late landing clearance comes once over the threshhold. Nevertheless I always called visual in these circumstances and was switched to Tower. In this case that did not happen so the chance to contact the pilots was missed.
On finals one night I did witness the converse scenario to this incident, when an A320 was cleared to line up and take-off in front of me. He then proceeded to taxy onto the closed main runway (32L) of which the second half was still a construction site. Fortunately the Tower spotted this before any further drama could unfold.