O executável é de 32 bits e sua instalação Debian é de 64 bits. Você precisa instalar as bibliotecas de 32 bits apropriadas. Tente instalar ia32-libs primeiro, acredito que é assim que você obtém as bibliotecas de 32 bits no Debian.
Acabei de instalar o EAGLE na minha caixa de chiado do debian, mas não consigo iniciar o executável:
joe@mybox:/opt/eagle-6.4.0/bin$ ll
total 18264
drwxrwxr-x 2 joe joe 4096 Jan 7 17:02 .
drwxrwxr-x 10 joe joe 4096 Jan 7 17:02 ..
-rw-rw-r-- 1 joe joe 1810 Jan 7 06:04 designlink22.png
-rwxrwxr-x 1 joe joe 15507004 Jan 7 17:02 eagle
-rw-rw-r-- 1 joe joe 43100 Dec 13 2011 eagle.def
-rw-rw-r-- 1 joe joe 827283 Jan 7 17:02 eagle_de.htm
-rw-rw-r-- 1 joe joe 362467 Jan 7 17:02 eagle_de.qm
-rw-rw-r-- 1 joe joe 743831 Jan 7 17:02 eagle_en.htm
-rw-rw-r-- 1 joe joe 336086 Jan 12 2012 eagle_hu.qm
-rw-rw-r-- 1 joe joe 718 Dec 13 2010 eagleicon16.png
-rw-rw-r-- 1 joe joe 2924 Dec 13 2010 eagleicon50.png
-rw-rw-r-- 1 joe joe 226206 Jan 7 17:02 eagle_zh.qm
-rw-rw-r-- 1 joe joe 4029 Dec 13 2011 freeware.key
-rw-rw-r-- 1 joe joe 603 Dec 13 2010 pcb-service.png
-rw-rw-r-- 1 joe joe 1768 Apr 21 2008 platforms-lin.png
-rw-rw-r-- 1 joe joe 1907 Apr 21 2008 platforms-mac.png
-rw-rw-r-- 1 joe joe 2019 Apr 21 2008 platforms-win.png
-rw-rw-r-- 1 joe joe 324383 Jan 12 2012 qt_de.qm
-rw-rw-r-- 1 joe joe 272162 Jan 12 2012 qt_hu.qm
joe@mybox:/opt/eagle-6.4.0/bin$ ./eagle
bash: ./eagle: No such file or directory
joe@mybox:/opt/eagle-6.4.0/bin$ file eagle
eagle: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.4,
BuildID[sha1]=0xbc1347e883e2d0da68c6dec32f822d7fac2b52a6, stripped
joe@mybox:/opt/eagle-6.4.0/bin$ uname -anr
Linux mybox 3.2.0-4-amd64 #1 SMP Debian 3.2.41-2 x86_64 GNU/Linux
joe@mybox:/opt/eagle-6.4.0/bin$
Eu não tenho uma única pista, porque isso está acontecendo. Alguma idéia?