I think the article you link confuses two different things- bug tracking system is not the same as the bug handling process.
Saying "If it is non-critical, you drop it." doesn't mean you don't track the things you are leaving, tracking can be done in using any system you like and in this case it's the Kanban board. The opposite is also not true, you can ...
The removal of bug tracking doesn't mean the removal of bugs !
In fact the ability to find and spot bugs (your skills) are more important and timely than ever.
It can feel very comforting to log bugs. They prove (validate) that you found stuff. They add to a mountain of work that needs to be done. See that backlog grow! Unfortunately we're moving away ...
Agile testing relies on a number of key concepts. Two of them are:
The Test pyramid
This provides a guide for having a large number of good unit tests, a medium number of integration tests and a small number of the slow and brittle (by their nature) UI tests.
Agile Testing Quadrants
Similar to the pyramid, another representation of the various different ...
I am not sure true Agile testing techniques exist. Some testing techniques are used and work well within the Agile context, others don't.
Common agile quality practises, part of the technical excelence princible:
Specification by Example
Test Driven Development
Whole team approach
Some techniques that might help: