Yes, it includes intragovernmental debt. Are you implying that we don't have to pay back the debt we borrowed from the Social Security program, that which is promised to others? The Federal Government owes that money to the people it's promised, right?
Claiming it's not "real" debt means that when I take out a loan and guarantee it with money in my savings account, then the loan doesn't count as an outstanding debt. It's a debt and counts. Add up your debts, add up your assets, and you'll find your net worth.
Go to a bank, show them the above, and ask them if they will "ignore" your outstanding debt you backed with existing assets (bank account). They'll laugh you out of the bank. GAAP pretty much requires you to count that debt (of course, the Federal Government chooses to ignore GAAP because it's politically embarrassing - never mind that if you didn't use GAAP for your own tax reporting or public financial disclosure the same Federal Government will prosecute you and toss you into Federal PMITA Prison).0
In the case of the US Federal Government revenues, our debts piled up a little over $1 trillion more than our assets last year - and always piled up more than revenues, during the Clinton years.