Arsene Wenger has a very well-defined way he likes to have his teams play; we all know that. His style of playing relies on fluidity, on passing from the midfield, and on creating space with lots of quick, short passes. What his style doesn't rely on is the traditional "target man" up front, the guy that either lurks in the box and waits to poach a goal or who gets himself free to receive a headed ball from the wing and nod it home.
With Olivier Giroud being the only out-and-out striker Arsene has, there has been a chorus, both over the summer and now, of ARSENE YOU NEED TO BUY A STRIKER WHAT IF GIROUD GETS HURT etc. Arsene, as Arsene is wont to do, ignores that chorus, because he understands his system better than we do and he knows how to make it work.
The Guardian has a very good summation and analysis of Wenger's philosophy today, and it contains this quote, which sums Arsene up better than I could:
Such has been the chorus of complaint, the barking sense of absolute conviction that Wenger must, must buy a striker that, as the transfer window flutters by, one thing above all seems patently clear. He isn't going to buy a striker. It is best just to get used to this fact, to acknowledge that this is a man who would rather die on his feet in the throes of a soft-shoed sideways dink, than live on his knees if that means being obliged to perform a series of hopeful diving headers.
We can all sit here with our Football Managers and our FIFA's and go 'THERE'S A HOLE IN YOUR ROSTER SO YOU'D BETTER PUT A STRIKER IN IT BECAUSE A STRIKER IS NECESSARY', but if you look at the way Arsene prefers to play, a striker is not actually necessary. Sure, there needs to be eleven players on the field, and at least one of those players should be the closest person to the opposition keeper, ready to receive a pass, but to expect that person to be nothing but a striker is to expect Arsene to be able to zip up his jacket on the first try.
In the modern game, players are expected to be the human equivalent of Swiss Army knives. The era of quoting formations and positions as literal expressions of a player's ability ("he's a classic number nine", "where does he fit in a 4-2-3-1" or "this team is best suited for a 3-4-1-2", etc) is rapidly, and mercifully, coming to an end, because in this day and age, defenders should be able to attack a little (as Ashley Cole first demonstrated), midfielders need to defend a lot, and forwards, well, they need to be both forward and midfielder, and occasionally to be able to defend.
So to me, at least, it doesn't matter whether someone is a striker in the classical sense - what matters most is whether they fit into the system, and players like Julian Draxler absolutely do.