Hello,
Yes, you can also write "Bestellst du auch etwas zu essen?" which is the standard form.
The shortening is not necessary, it is a colloquial form, which is that in everyday context, people might say "Bestellst du auch was zu essen?" instead of "Bestellst du auch etwas zu essen?".
Some other instances of colloquial shortening are -
Kugelschreiber - Kuli (ball-point pen)
Pullover - Puli (sweater)
Universität - Uni (university)
Hope this helps.