DBX files will not open directly once Outlook Express is missing, because that format was made for the old Outlook Express mail store. New Outlook versions need the data in PST or another supported format.
If you have only the backup files, first check the folder for Inbox.dbx, Sent Items.dbx, Drafts.dbx and any custom DBX folders. Work on a copied set, not the original backup, because old mail files can be the only source of years of emails.
In this situation, try a smart offline tool like GainTools DBX to PST converter software. It can help turn those old Outlook Express backup files into Outlook readable PST files with proper control over selection, preview and local saving. After conversion, you can open the PST in Microsoft Outlook and check the emails.
A safe step is to test the free demo first with 10 emails from each DBX folder. Check dates, attachments, sender details and folder names before converting the full backup.