Close. Consider "hookee" as the object being hooked. Strikee is the object being struck, etc. Old English.
Both interesting theories but I don't buy it. The lapse of time between recorded appearances can be explained by two factors: first, how often is anything of a non-"official" nature for centuries, as sport, remarked upon or discussed especially in a time when the activity was frowned upon as possibly leading to disorder (as soccer/football can to this day) and/or a challenge to organized religion? Even in Galway it was mentioned only because the game became the object of the law. By the 1700's-1800's, as part of an Enlightenment pattern you start to see games discussed seriously, same thing in France. In effect they became the object of social history but it took centuries for this way of thinking about it to emerge.
Also, we know that terminology varied as indeed in any sub-culture, where different terms can be used to mean the same thing. This is especially so before a standard set of rules emerged for hockey - and before spelling was standardized even for standard English. Hockey could have different spellings under these conditions, just as hurly/hurling/horling did. Hocky as a variant is recorded too.
It makes sense (to me) that a name for the stick became, in time, applied to the game - and whether from hook or hocquet seems a distinction without a difference - and displaced other names such as bandy ball and hurly. And no question the 1527 law is calling the sport hurly but it is calling the main implement used a hockey stick.
Why the name of the stick became applied to the sport is hard to say, habit, maybe a way to differentiate the game as played in England, or as played around London by different classes than in the Gaelic lands, or just happenstance of some kind, explains it.
Gary