It does generate a long-term representation, the issue being that even with context and timestep specific data, that embedding is too general to make a good representation.
Sports are particularly problematic because almost all teams and statistics regress to the average at some point, meaning your generated future timestep context clues don't really help modify the embedding.
You're also dealing with variation within a season (injuries, better play, etc) and between seasons (personnel changes, rule changes, new stadiums, etc). So a team might have 4 seasons of above average performance, and then abruptly be the worst team in the league the next because they lost their coaches and star players.