Ah there are three (and more) ways. Don't use the Launch button--1) use the player's own "File->Open" command.
2) Drag-and-Drop: Use LW's Explore button to find the files on your hard drive for their location (Probably in Home->Shared). You can drag them from there onto the player's icon in the dock or Applications folder.
3)With Get Info: to set them to open in the player of your choice, find the file on the hard drive, click once to select it, then use the Finder's File->Get Info command--cmd-I--to call up the Get Info box. There you'll see the options to "Open With", where you are asked to choose/add the player you want . You can also make that player the Default for all similar files.

Setting defaults via Get Info is the best long term solution. This is what determines LW's Launch button setting.

Hope that helps--learning filesharing AND a new computer can be confusing. Luckily both OSX and LW make it pretty easy.