SELECT t1.team_name as Home, g.home_score, t2.team_name as visitor, g.visitor_score,
g.game_date, g.game_time, g.venue
FROM games g, teams t1, teams t2
where g.visitor = t1.teams_id
and g.home = t2.teams_id
order by g.game_date
you have t1.team_name as Home, but you're joining t1.teams_id to g.visitor!
also, you could improve on the query structure a little bit...
SELECT home.team_name as home
, away.team_name as visitor
JOIN teams as home
ON home.teams_id = games.home
JOIN teams AS away
ON away.teams_id = games.visitor