It looks like you are on the right track in thinking that this is a licensing issue. Here is the applicable section from the ESRI Help documentation about Maplex: Licensing and the Maplex extension
I think this section is the clearest explanation of what you are seeing in the included images:
Viewing Maplex labels without a Maplex license
At ArcGIS 10, you can view Maplex labels in a read-only state using an
ArcView or ArcEditor license without a Maplex extension license. You
will be able to view the Maplex parameters that created the labels,
but you will not be able to edit them.
The documentation is a bit confusing in that it differentiates between having a license for Maplex, and having an ArcINFO level license of ArcGIS.
If you have the license for Maplex, you will have the full functionality of the extension regardless of what ArcGIS license level you are using.
The ArcINFO license of ArcGIS is the only one that gives you the full Maplex functionality regardless of whether you have a Maplex extension.
Are you sure you need to have the Maplex functionality? It is possible to do some pretty complex labeling using the standard label engine. You just have to make a few more tradeoffs, but it is definitely possible. Since you are using an evaluation license anyway, it is worth looking at what your basic functionality is.
If you are able to wait for ArcGIS 10.1, the Maplex labeling has been moved from an extension into the core functionality of the program: What's new in Maplex for ArcGIS 10.1