and during the real gameplay, unfortunately, the game is really slower (on harder moments)...
So, where can be the problem?
I can confirm that this is a good idea.
The Q3 engine was never designed for 64bit and/or multiple CPUs.
I don't understand (though i'm a C/C++ programmer

), if the source code is written for 32bit processors (doesn't use 64bit data types) than compiling it for a 64bit processor only gives it more address space in memory. If the code is written well there should be no difference in programme's performance. I had no errors during compilation, so the code is good, but maby there were some warnings?
Maby there is a way to "redesign" the code for 64bit processors, and I am sure that it is worth the effort.