All strict->import (normally called via use strict) does is modify global var $^H. The compiler uses $^H to determine if it should throw strict errors, among other things.

The compiler localises $^H to the block being compiled. This is what produces the lexical scoping of the pragma.

{ # $^H is localised by the compiler
  # when it compiles this.

   use strict;  # Changes $^H
   ...

} # $^H is restored by the compiler
  # when it compiles this,
  # undoing changes in strictures.
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In your example, the block being compiled when strict->import is called is your script's file block, so the strictures stay in effect until the end of the file.

Similarly scoped hash %^H is available to modules that want to be lexical pragmas without having to fight Perl for the limited bits in $^H.

Update: Added code example. Added mention of %^H.