two things:
first, try not to put osax-based commands inside of application tells. 'say' is a command in the standard additions osax, and is not guranteed to work when called in any context other than the main script context. rewrite like so:
tell application "SpeechRecognitionServer"
set theResponse to listen for {"yes", "no"} with prompt "Hello. Do you like me?"
end tell
if theResponse is "yes" then
say "I like you, too."
else
say "I don't care whether you like me or not."
end if
second, and more to the point, you need to hold down the escape key (by default) to get the speech recognition server to listen. you'll know it's listening because the microphone will go from gray to black and moving arrows will appear pointing in at the mic.