Okay, I was able to solve it, even though I don't really understand how.
The parameter IfcDescription is (and was) available in the project, I've checked Project Parameters and it is (and was) there, relaying to Structural Framing.
I reproduced the steps from the other project, which were:
1 - Link the IFC;
2 - Bind the link (I did it originally to see if the geometries would show correctly);
3 - Delete the resulting Group as it was a mess;
4 - Re-link the IFC;
The parameters from the IFC were only available on the first file because I tried binding, which didn't work properly (but imported all the parameters of the IFC file into the Revit project), so I was able to filter by those parameters, which would otherwise be unavailable to me.
After completing the 4 steps above, the parameter IfcDescription was duplicated. One of them works, the other don't. They probably have different GUID given that are different IFC files.
My guess is the first one was imported with the filter, but is "different" from the one in this IFC file, hence the mess.
Thanks for your help @SteveKStafford .