Vlad, this parses your string into a Perl hash, after doing some tweaking to your JSON string.

#!/usr/bin/perl 
use strict;
use warnings;
use JSON::PP;

my $json_text = '';
# read string from __DATA__
while(<DATA>){ $json_text .=$_ }

# work around javascript eval's
$json_text =~ s/^(\w+:) \(.*$/"$1": 0, /gm;
# fix date
$json_text =~ s/:\s*new Date\((\d+)\)\s*/&epoch2timestring($1)/ge;
# fix hashes
$json_text =~ s/^(\w+:) "{(.*)}",/"$1": {$2}, /gm;
# fix remaining fields (should be quotes)
$json_text =~ s/^(\w+):/"$1":/gm;


my $perl_scalar = JSON::PP->new->relaxed->allow_singlequote->allow_bar
+ekey->loose->decode($json_text);

use Data::Dumper; 
die Dumper($perl_scalar);

sub epoch2timestring{
        my ($e) = @_;
        $e=~s/.{3}$//; # eat 3 last digits
        my $result = scalar localtime($e);
        return ': "' . $result . '" '; # gmtime() ?
}


__DATA__
{
is_touch: ('ontouchstart' in window), 
repository_urls: ["publisher_view2_videossp/PublisherView_videossp2"],
origin_repository_url: "publisher_view2_videossp/PublisherView_videoss
+p2",
workbook_repo_url: "publisher_view2_videossp",
publish_date: new Date(1431654084199),
tabs_allowed: false,
showTabsWorkbook: true,
mobile_app_cookie: "",
current_project_id: "7",
current_sheet_name: "",
current_sheet_type: "", 
current_workbook_name: "publisher_view2_videossp",
current_workbook_id: "1548",
current_view_id: "2713",
sheetId: "PublisherView_videossp2",
showParams: "{"revertType":null,"refresh":false,"checkpoint":false,"sh
+eetName":"","unknownParams":"zone_id=6290&ac=a9aef098062f9646bd1638d0
+c6054c7b&account_id=62&Start_Date=2016-07-27&End_Date=2016-08-03","la
+youtId":""}",
stickySessionKey: "{"isAuthoring":false,"lastUpdatedAt":1470316180805,
+"workbookId":1548}",
}
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edit: added missing "my" that got lost in copy/paste, now it runs...