I have not seen any indication that private messages are included in this. As the person indicates, phone numbers are only included if they were posted on Parler by the users themselves, but yes from what I can tell the IDs are the most "private" part of the leak. Although one could argue that they are still "public" given that Parler publicly exposed the information.
The article itself never defines "messages" and, from context, it seems like they referred to users' [public] posts as "users' messages" -- not DMs/PMs.
EDIT: A clarification on Twitter from ~9h ago:
"since a lot of people seem confused about this detail and there is a bullshit reddit post going around:
only things that were available publicly via the web were archived. i don't have you e-mail address, phone or credit card number. unless you posted it yourself on parler."
>I am now crawling URLs of all videos uploaded to Parler. Sequentially from latest to oldest. VIDXXX.txt files coming up, 50k chunks, there will be 1.1M URLs total: https://donk.sh/06d639b2-0252-4b1e-883b-f275eff7e792/
>This may include things from deleted/private posts.
"Private" posts are posts shared to specific circles AFAIK, not the classic definition of 1:1 DMs. They're still semi-public, a bit like Google+ Circles.
By "messages" they mean public posts directed at other people, like I'm 'messaging' you right now. It's a misleading title that was meant to sensationalize the 'hack'. It seems like all this amounted to was a simpler way to scrape public posts.