You can use wildcards in qmake .pro files, to save having to maintain a list of all file names.
For example,
SOURCES += *.cpp
Each time you run qmake, that pattern *.cpp
gets expanded in to the current list of files matching the pattern.
You can also use -=
to remove file names, if you have a particular filename that you wish to exclude.
For example:
SOURCES += *.cpp
SOURCES -= main.cpp
Edit
I almost suggested in my earlier answer that you introduce a library, using qt's lib template, to contain your common code.
Then your build structure would look like this - assuming that you can move files around, from app/ to lib/:
game
game.pro
app
app.pro
main.cpp
lib
lib.pro
Entity.h
Entity.cpp
Entity.o
moc_Entity.cpp
moc_Entity.o
tests
layer
layer.pro
tst_Layer.cpp
You can find some info on library projects in "Building a Library" on the Qt website
If, for some reason, you can't move your files around, then you can introduce a new directory for the library, and have it pull in source files from the app directory - but that is definitely more faff, and more confusing:
game
game.pro
app
app.pro - builds only main.o
main.cpp
Entity.h
Entity.cpp
moc_Entity.cpp
lib
lib.pro
Entity.o
moc_Entity.o
tests
layer
layer.pro
tst_Layer.cpp
Edit 2
One problem you have is you are putting object files in to the LIBS variable, which defines what libraries your code will link against. So that'll be why you are getting errors with those files.
Try changing those LIBS uses to OBJECTS instead, and it may work.
If not, have a read of this thread, which is asking pretty much the same thing.
In particular, see the answer by ChrisW67 of '13th May 2012, 10:14' which begins;
Try:
OBJECTS += f1.o f2.o f3.o f3.o
although I think that, if you have the source, building it into your app directly or via a library is a better option.