It seems impossible to export records that you drill down into in campaign reports. For example, if you drill down to unique opens and hover over campaigns and select export, which is how I was told you do this, it exports only that screen of 20 records. i cant imagine many people expecting that. This should export all records as you can select the date range or gibe you the option to list all records on screen before you choose export. Having to go through hundreds of screens to export all records does not seem like that was the intended result of this functionality.
Secondly, it would be very handy to mimic the create a custom report where you can select campaigns, select a criteria like "opened" and then run the report and get the export of the data, not just the stats. If that functionality exists, I am unaware of it. It seems like maybe a segment could be created and then exported but there does not seem like the ability to select users who opened a group of campaigns (for ex, containing "payment") in one easy fashion. You'd have to create a rule for each campaign. The functionality in the custom reports how you select campaigns would be useful here.
The pathway you mention is the one for just quickly exporting the contacts you see on screen. We put this feature in at clients' request who only wanted to export the screen and not the full report.
If I understand your intent which is to get the full export, then my response is that you should just open up the campaign details page and use the export option that's there. This gives you the full export of data within the date range that you specify.
Vice President - Product and Client Success
Maropost Marketing Cloud