Yes, you are using a modern dictionary, which lacks the context of the time in which the phrase was written.
I guess you missed the Supreme Court decision that 2A is an individual right?
You probably also don't realize that the state militia argument was a fairly recent (within the last 100 years) phenomenon. The Second Amendment had been assumed to apply to individual rights until then. The state militia argument didn't gain any traction until around the same time that Congress started its trend of ceding more and more powers to the Executive.