The only way I would say a game is not-strategic is when you can reliably win against an opponent by spamming 1 or 2 unit types or using 1 strategy without responding to the actions of the other player. If you could win every Starcraft 2 game you played by building nothing but zerglings then it wouldn't be strategic, but that's not the case
Sure you might be able to get a way with it a few times in the lower brackets but upper level players with have hellions waiting a choke points and air units flanking you to put you in deep shit. There is usually a counter strategy for every unit spam in that game and the only types with few weaknesses like Carriers, Battlecruisers and Broodlords/Corrupters can be countered with by strong players with relative ease.
So I guess the point is that the only way I would consider a genre nonstrategic is if a certain player strategy is simply impossible to counter.
Sure you might be able to get a way with it a few times in the lower brackets but upper level players with have hellions waiting a choke points and air units flanking you to put you in deep shit. There is usually a counter strategy for every unit spam in that game and the only types with few weaknesses like Carriers, Battlecruisers and Broodlords/Corrupters can be countered with by strong players with relative ease.
So I guess the point is that the only way I would consider a genre nonstrategic is if a certain player strategy is simply impossible to counter.