The “something” here refers to inner experience (something similar to Kantian “aperception”.
The tricky bit is that “to be” is not an ordinary verb like fly, eat, or echo-locate. And “‘being an organism’” is — in the context of the paper — about subjective experience (subjective to everything except the organism.
To put it another way, the language game Nagel plays follows the conventions of language games played in post-war English language analytic philosophy. One of those conventions is awareness of Wittgenstein’s “philosophical problem”: language is a context sensitive agreement within a community…
…sure you may find fault with Wittgenstein and often there are uncomfortable epistemological implications for Modernists, Aristotelians, Positivists and such…then again that’s true of Kant.
Anyway, what the language-game model gives philosophical discourse is a way of dealing with or better avoiding Carnapian psuedo-problems arising from an insistence that the use of a word in one context applies to a context where the word is used differently…Carnap’s Logical Structure of the World pre-dates Wittgenstein’s Philosophical Investigations by about 25 years.