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."
https://twitter.com/donk_enby/status/1348666166978424832