How are profiling- and tracing -techniques used in Game Development?

There are two kinds of data we can profile, at the high level:

1. We can profile the execution of the program itself -- what functions are called when and where, how long they take, and what impact they have on the environment (allocations, locks, threads spawned, et cetera).

2. We can profile what the user is actually doing with the program -- where they are in the game when they die, where they are when they earn the most experience, what they spend the most money on, which skills they use most often.

These aren't fundamentally different operations, really, although the type of data collected by each operation is pretty significant. The type of data collected by the first technique is generally reusable across many programs, whereas the second type of data tends to be more program/game specific (experience may not even exist in a particular game, for example).

You have the right terminology for this kind of technology -- "profiling," "tracing," "user monitoring" and such are all appropriate terms. The technology itself is fairly straightforward to implement as well. The most basic approach just involves instrumenting code by calling a function that collects the desired data. You can then write that data to a log file or (most usefully) send it to a database for later querying and report generation.

Code coverage, which you mention at one point, is a little more complex and difficult to get right (especially in more dynamic languages). It is more akin to the first technique, that is examining the state of your code rather than how users use your program.