I have to think this is more aimed to help recruiting against the other non-UConn schools than against UConn.
Over the last 5 years, only UConn has had better success winning at the college level and producing pros (maybe Baylor is arguable). At best, ND can use this line of reasoning as "We can also send you to the WNBA and we also offer that they don't".
But UConn only takes so many kids and some kids don't like UConn for whatever reason, so it's not like every ND target is also in UConn's crosshairs - many, but not all.
Re the timing, keep in mind that the September 1 was the first date schools are allowed to talk to high school juniors and home visits to those juniors are coming up. This is as much or more aimed at the Megan Walkers of the world than at Lauren Cox.
Although this recruiting brochure will of course be used against other schools I think it is aimed at competing specifically with UConn. Just look at the content:
The Coaching: quotes from WNBA coaches about how well ND develops its players. Player development and producing WNBA-ready talent is a strength of Geno and the UConn program.
The Network: former players come back and practice with the current team. How often have we heard about the UConn alums coming back to practice with the Huskies or the UConn club in the WNBA? One program from the south included the practice issue in an NCAA complaint.
The Competition: ND plays in the tough ACC and plays schools from other P5 conferences. UConn's conference affiliation is a weak spot and this brochure subtly goes right after that weak spot.
Style of Play: Up tempo, style of play produces players who are WNBA-ready. Again, no school produces more WNBA-ready players than UConn.
Both schools competed for Samuelson and Collier and are now competing for Cox, Walker, Jade Williams and likely others.