A quick look at RTT suggests:
Chesterfield is very little changed from the present (ie a fair number non stopping)
Wakefield loses several calls on Saturday 15 June (and presumably other Saturdays, but not yet showing?), none on weekdays.
Basingstoke has a random one on 15/6 and Winchester none that I can find. Obviously that is incomplete, but are we reading too much into a press release?
It might very well be that the changes haven't yet been enacted, if they're late-notice. But yes, skipping Basingstoke is absolutely ridiculous as it allows connections to/from lots of SWR stations. It also forms a key part of the Basingstoke-Reading service, particularly on Sundays when GWR only run 1tph.
It's disappointing that rather than properly fixing the capacity problem - which would have been easily doable by transferring all the Avanti 221s to XC - they are only getting 12 of them and are attempting to "become a more IC operator" as I believe one of their Managers put it. This completely overlooks the fact that short hops around cities make up the majority of their passenger journeys (by volume, at least).
This is far from the only move they've taken to try and force local passengers off their trains. See also: making their trains "reservations compulsory" between Birmingham and Wolverhampton and then refusing to issue reservations for that journey, pretending the train is "sold out". I get what they're aiming at, but there simply isn't enough capacity or frequency on other services!