Terminal app on OSX stores the information about its windows and content in its state files in Library/Saved Application State/com.apple.Terminal.savedState .

I did the backup of the file before the crash to be able to restore my data, but I don't know how to read it now (as Terminal refuses to use it). It starts with: NSCR1000 as below:

$ hexdump -Cn8 ~/Library/Saved\ Application\ State/com.apple.Terminal.savedState/data.data 00000000 4e 53 43 52 31 30 30 30 |NSCR1000|

It's used by windows.plist file which can be decoded by:

plutil -convert xml1 -o windows.plist windows.plist

What kind of method I can use to read that .data file? Or where do I start?

$ strings data.data | head -10 NSCR1000 p+5v 0>[t kJX6X @NSCR1000

This file is automatically generated by Terminal app when you start and start typing something, so the terminal data is stored there.