You are using 64-bit linux, but Machinarium (Flash exactly) is avalaible for 32-bit. You can launch and play Machinarium in 32-bit mode using 32-bit libraries if you have them installed
linux32 Machinarium
Additionally all required libraries are to be provided by you system. In ubuntu it is enough to
sudo apt-get install ia32-libs
but I have not idea on equivalents to RedHat. You also mentioned you are not root, then probably wine is the best option for you.