What he said is that on some other architectures 32bit is more efficient than 64bit. This is not true for x86, because they fixed some architecture shortcomings while implementing 64bit (more registers for example). Because of this on x86 64bit code is faster than 32bit code.

On architectures like MIPS for example 32bit code is faster than 64bit code. This has to do with pointer sizes, which are bigger in 64bit and use more memory and more cache and take more bandwidth on the bus. So the 64bit code is slower.
Usually the kernel is 64bit, but most of the libraries are compiled as both 32bit and 64bit. If you need more memory than 4GB, you compile as 64bit, otherwise you compile as 32bit. The increased memory size you can address is the only advantage of 64bit on systems like this.

"It" being some version of Opera.
To put the list into perspective a bit, lets take a look at the versions of Opera that run on some of these systems:
QNX: Opera 6.01b (which is a beta release). The last stable version for QNX is Opera 5.2.1.
OS/2: Opera 5.12.
BeOS: 3.62.

I somehow don't get to see any other releases. The server probably thinks I have one of the above systems (I have BeOS, but I still should be able to download Opera for any system I want to).
The BeOS version is unusable on the web today. It was only marginally useful when it was still new.
I don't know about the other two, but the story is probably somewhat similar.

Just because you like open better does not mean that infringement of the GPL (or BSD) license is worse.

Perhaps you would like to give some real arguments as to why infringement of an open source license is worse that a closed source license.
They are both equally protected by the law.