SYSTEM PATHS MAY VARY!
The game doesn’t have a default windowed mode so you have to edit the config file to make this possible. You can find this config file by going to your home directory and navigating to Library/Preferences/Firaxis Games/Sid Meier’s Pirates/My Games/Game. Open the "Config.ini" file with TextEdit and add the line "fullscreen = 0" to the bottom of the list. Then save the change you just made to this file, quit text edit, and you’re ready to go. Obviously you’ll want to make sure the game’s resolution is set lower than that of your monitor’s resolution or else the window won’t fit. For example, my monitor is set to "1344 x 840" and I set Pirates to "1280 x 800".
Source
I remembered having to do this once.
It all depends on where your SAVE file is located. Be sure to check your documents FIRST then the SteamApps folder, as this would be the install dir, NOT THE SAVE DIR!
For Windows Users:
Hold WinKey+R then type notepad.exe C:\Users\{YOUR USERNAME HERE}\Documents\Firaxis Games\Sid Meier's Pirates\My Games\Game\Config.ini
IF NOTEPAD CANNOT FIND THE FILE THEN START SEARCHING:
For windows Vista and up: C:\Users\{YOUR USERNAME HERE}\Documents\Firaxis Games\Sid Meier’s Pirates\My Games\Game
MAY BE your path.
It may also be in C:\Program Files(x86)\Steam\SteamApps\common\
For Windows XP and below (Cause We're all hipsters/old farts that way): C:\Documents and Settings\{YOUR USERNAME HERE}\My Documents\Firaxis Games\Sid Meier’s Pirates\My Games\Game
How can I play Sid Meier's Pirates! in Windowed Mode?
and removed the stuff about recording, but otherwise FRAPS is the one that actually will catch the process and record the game output without having to edit any files.