Adding one transforms it from the range [-1 1] to [0 2] . Multiply by 2^12 to get a value in the range [0 4096] . Divide by 2 to get [0 2048]. Which is suitable for transmission over a digital interface using unsigned bits.
(The way they use OFFSET looks a bit dubious to me though. But it doesn't affect anything when OFFSET is 0.)
If 1 were not added to y then you would start having to transmit values in the range [-2048 2048], and then you would start having to argue about which of the three major representations you use for negative values.