The article has a lot of lead up to the main point - he was on the path to even more special things in addition to the World Cup winning goal. And the injuries that were thought to be hindering him turned out to be related to the long standing rare muscular disorder. That pretty much answers the title.
The real question should be, could Gotze have rivalled Messi in any capacity had he also started taking some sort of medically reasoned dose (not necessarily HGH) at a younger age..could he have staved off some of the injuries with a proper diagnosis?
I think he was actually already on the decline when he scored the goal vs Argentina. That season was when his disease began to affect his performances. The young Götze was an incredible dribbler but as soon as he arrived in Munich, he kind of lost that quality. Guardiola would never use him on the wings because he lacked the required pace. Götze was always compared with Neymar and in the WC 2014 I remember Neymar stepping up big time and everybody wondering why Götze played so cowardly. Now I think he intuitively adjusted his playing style to his declining physique.
Could he have rivalled Messi? I don't think so. In terms of close control, footwork and footballing brain, probably yes. Besides that he could convert his abilities into results from a very young age and was never really a show pony but frightingly effective. He also is a very, very good finisher, unlike exemplarily Hazard. But he never had this incredible acceleration of Messi and this is not because of medication but because of their body characteristics. I recently read Messi is the footballer with the shortest legs compared to his upper body, giving him an extremely low center of gravity. Götze lacked that part. At one point for Dortmund, he was Europe's most successful dribbler (I think with five dribbles per game) aged 18 or 19 but this physical prowess was never part of his game. I think Iniesta or Zidane would be a much better comparison.
But there's still time. Reports said that now his disease is diagnosed and he gets treatment, there is no reason why he should't be back to his best. Some matches of him looked really promising. If he is able to lose some kilos again it might actually happen. Would be amazing, he was my favourite player to watch in his first Dortmund episode.