Hmm. I don't know enough about midi to say which players would support that, and I don't have Logic, so I can't check its scripting support.
My GUESS would be that Logic would support similar phrases in AppleScript. "open <file>" is virtually universal. "document <x>" is virtually universal. The "play" command is natural for any program that deals with audio or video files. Have you tried just changing it to say tell application "Logic" ?
As a general AppleScript tip, you can see any program's scripting dictionary by opening the program file with AppleScript Editor (either drag the application to the Script Editor's Dock icon, or go to File > Open Dictionary).
If Logic has no AppleScript support whatsoever, you can, as a sort of last resort, use keystroke and/or mouse click simulation. Many applications use the space bar to play/pause, which could be triggered in AppleScript like so:
Replace " " with whatever keystroke triggers playback in logic. If it's a combination, you can say something like:
tell application "Logic" to activate
tell application "System Events"
keystroke " "
keystroke "p" using command down