`RANDOM` isn't a command, it's a variable. Just one set by the shell and a bit of a special one:
> RANDOM Each time this parameter(*) is referenced, it expands to a random integer between 0 and 32767. Assigning a value to this variable seeds the random number generator. If RANDOM is unset, it loses its special properties, even if it is subsequently reset.
Something like `echo "$RANDOM"` is exactly how you'd use any variable, like the more "normal", `HOME` and `BASH_VERSION`. Of course `${RANDOM}`, with braces and not regular parentheses works too.
Being able to use it in an arithmetic expansion without the `$` is also a feature of the arithmetic context, and works for any variable:
> Within an expression, shell variables may also be referenced by name without using the parameter expansion syntax.
(e.g. `x=4; echo "$((x*x))"` prints `16`)
(* You can ignore the variable vs. parameter distinction here.)