I would like to add this thought. Defense is supposed to prevent you from suceeding, correct?
Therefore "sports" like golf, skiing, Nascar, cycling can be construed to have defense.
For example, the course itself is the defense in golf; doglegs, narrow fairways, sandtraps, water hazards.
Cycling and Nascar share some qualities, both are predominately an individual sport but there is a team element and certainly defense can be argued when the cut each other off to prevent passing or a team mate blocks for another and in cycling, the course again plays defense by being difficult to complete.
Skiing falls along the same lines as golf, the course provides the defense in the sense that the grade of the slope, having to pass through gates, weather conditions all acting in concert to prevent the skiier from finishing, etc.
As for being a game, timed events are a game, it's called beat the clock. I would change your definition to objective scoring in place of game thus ruling out all judged events.
I agree that to be a "sport" there has to be athleticism, an objective scoring system or game as you stated (goal, points, timer, basket), an element of offense and defense and it has to be a competition, meaning winner and losers.