Is it possible to have the computer game 2142 downloaded onto a portable hard drive not the computer and play it without transferring it onto the computer

Technically yes. When installing BF2142 you can specify the installation directory as the USB drive. However this will only work provided the USB drive keeps the same drive letter and it wont work on other computers. This is because the process of installing the game puts entries into your registry that the game requires to function. This isn't the case with all games, older games such as Diablo and even modern ones such as EVE online will work fine on any computer and can be installed on USB sticks etc. It is worth noting that the transfer speeds from a USB hard drive are not as fast as an internal drive and also require a lot of CPU so BF2142 might not be the best game for this setup.