I’d suggest that if he didn’t support the CSC’s mission, he would resign as a member of it:
The mission of Discovery Institute’s Center for Science and Culture is to advance the understanding that human beings and nature are the result of intelligent design rather than a blind and undirected process.
Swamidass holds to this idea too, but believes God indirectly used evolution to create the diversity of life. Craig may have adopted Swamidass’s stance on the issue. Whether you believe creation was direct or not, the statement still applies.
The DI does not capitalise “intelligent design” on their website, but it is clear throughout that they are talking about their ‘Theory’ of Intelligent Design, which I believe Swamidass rejects, not the more minimalist idea that any theist would accept.
Addendum: I’m curious as to why you think it likely that Joshua has changed WLC’s views on ID. It seems unlikely that he is the first devout-but-Evolution-affirming scientist that WLC has encountered.
Given that Behe himself admits to common descent, it is unclear that what WLC said is outside the ID ‘Big Tent’, which includes everything from ‘Evolution but…’ to YEC.