The wikpedia page says the 2011 defense budget was $929 billion, out of a total $3,598 billion - or 26%. It's pretty hard to "dwarf" a budget item that large.
From your link:
Social Security, Medicare, and Medicaid expenditures are funded by more permanent Congressional appropriations and so are considered mandatory spending.
Mandatory spending accounted for 57.4% of total federal outlays in FY2012
Hmm, looks like the entitlements are rather more than twice as much in total as the military spending.
Note, by the by, again from your source, that "military spending" was inflated by including DHS and VA into it. The actual military budget was only about 80% of that.
Which would make the entitlements closer to three times the military budget.
Hmm, more than twice as much entitlements up to nearly three times as much entitlements, depending on how you count "military spending"...
Yep, looks like the guy you were responding to was right, doesn't it?