rpm is an acronym for Redhat Package Manger.
the title says it all.
rpm are for redhat and redhat based distributions of Linux.
what you want is .deb package for debian based distributions (like mint).
but the best way to install an application is to use synaptic.
You can find it under mintmenu--> install software.
then you can use the search function to find the package or just browse for it.
once you find the package right click on it and choose "mark for installation"
then click the apply button. accept any dependencies.
BTW you can't install packages while using the live cd, since there is nowhere to install them.