32 and 64-bit linux binaries are identical

These are alternative links on the Download page:

files.arduino.cc/downloads/arduino-0021.tgz (32-bit)
files.arduino.cc/downloads/arduino-0021-2.tgz (64-bit)

By looking at librxtxSerial.so, they are both 64-bit.

What is the problem, do they not work?

The problem is they are both 64bit, which doesn't work on a 32bit machine:

java.lang.UnsatisfiedLinkError: /usr/share/arduino/lib/librxtxSerial.so: /usr/share/arduino/lib/librxtxSerial.so: wrong ELF class: ELFCLASS64 (Possible cause: architecture word width mismatch) thrown while loading gnu.io.RXTXCommDriver
Exception in thread "main" java.lang.UnsatisfiedLinkError: /usr/share/arduino/lib/librxtxSerial.so: /usr/share/arduino/lib/librxtxSerial.so: wrong ELF class: ELFCLASS64 (Possible cause: architecture word width mismatch)
      at java.lang.ClassLoader$NativeLibrary.load(Native Method)
      at java.lang.ClassLoader.loadLibrary0(ClassLoader.java:1750)
      at java.lang.ClassLoader.loadLibrary(ClassLoader.java:1675)
      at java.lang.Runtime.loadLibrary0(Runtime.java:840)
      at java.lang.System.loadLibrary(System.java:1047)
      at gnu.io.CommPortIdentifier.<clinit>(CommPortIdentifier.java:83)
      at processing.app.Editor.populateSerialMenu(Unknown Source)
      at processing.app.Editor.buildToolsMenu(Unknown Source)
      at processing.app.Editor.buildMenuBar(Unknown Source)
      at processing.app.Editor.<init>(Unknown Source)
      at processing.app.Base.handleOpen(Unknown Source)
      at processing.app.Base.handleOpen(Unknown Source)
      at processing.app.Base.handleNew(Unknown Source)
      at processing.app.Base.<init>(Unknown Source)
      at processing.app.Base.main(Unknown Source)

To put it another way, arduino-0021.tgz at files.arduino.cc should match the copy hosted at arduino.googlecode.com.

As you did not fix the problem, I assume that you did not understand it, or didn't know how to fix it:

Problem:
http://files.arduino.cc/downloads/arduino-0021.tgz contains a 64-bit librxtx and a 32-bit avrdude. this does not make sense at all.

Solution:
you should just replace it with the correct archive from your google code page. ( http://arduino.googlecode.com/files/arduino-0021.tgz )