Empirical cumulative distribution function is a cumulative sum of frequencies of observed $x_i$'s divided by total sample size. Your data is a vector of values from $1$ to $1000$, where each of the values appears exactly once. This means that your "variable" follows a discrete uniform distribution, that has a flat CDF.
As you can see on the example below, it'd be different if you used other imput data.
x <- sample(0:1000, 1e5, replace = TRUE)
y <- rnorm(1e5)
def <- par(mfrow = c(1,2))
z <- c(1,2,5,7,12,14,19,25,100,250,300,301,500,800,900,901,1000)
Notice that in the second example distances between different values are different so no matter that each value appeared only once, the line is curved.