Mice that have been reconstituted with geneX-transduced cells
Your second interpretation is correct.  The mice have been reconstituted from stem cells that were "transduced" (using a viral vector) with a construct containing the appropriate geneX. The link gives comparison of transduction vs. transfection.

https://www.vectalys.com/blog/what-are-the-differences-between-transfection-and-transduction-222