More info about the map and the forest types here. The forest types are described in chapter 6.
The map does not necessarily show what kind of forest actually grows in different places, if any, but rather which forest type you could expect to find there naturally, if it would be forest. But it probably matches reasonably well with what actual forests look like, although most of Europe is of course not covered by forests.
Here's a map over forest cover in Europe:
Also in the Sauerland in the northwest of Germany where there should be oak or beech, it is often sprouce (or since a few years dead sprouce).