How to "require an answer" in a dialog in AppleScript?
Yes, it can be accomplished like this:

repeat
  set myAnswer to the text returned of (display dialog "Your question goes here." default answer "")
  if myAnswer is "" then
    beep
  else
    exit repeat
  end if
end repeat


Please let me know if this works for you.



Second version that tells the user what the error is:

repeat
  set myAnswer to the text returned of (display dialog "Your question goes here." default answer "")
  if myAnswer is "" then
    beep
    display alert "Please enter your answer to continue."
  else
    exit repeat
  end if
end repeat