Goals - a goal can make all the difference. As for the most important part in a team, that's the quality of the players. Without players who have the technical and tactical know-how, the coach's tactics are meaningless. Many times the quality of the players dictates the coach's tactics.
In the USA, none of those are parts of the game. They are three (tactics, technique, and mentality) of the four subject areas of coaching. The fourth area of coaching is fitness (and nutrition). Perhaps fitness is what you meant by training.
This guy has been pushing his app all over the Internet on all the coaching sites. He never makes a post on anything else.
In a match, the specific tactics used by a team is in my opinion the least important factor leading to success. Goals can be scored with simple tactics. Defensive tactics are easy to teach. Tactics are a poor substitute for lack of skill or lack of match fitness. And tactics more important than mentality? I think not. High fitness and high skills drive up the speed of play. In evaluating players, I think mentality and technique are the most important areas. You can work with players like that. You won't get anywhere fast with players deficient in mentality and technique.
My belief is that when they are starting out Technique is the most important. At senior level, one isn't more important than the others. At least in MLS, one of the "pillars" will get you in the league. To be a really good professional in the better leagues, you need to have a high level of all four.
That makes sense looking from the top down, but if you look at soccer from the bottom up you see something different. Consider that you have to break into the reserves before you break into starting 11. So you are looking at a pool of players larger than just successful professionals. To progress up a level, the first challenge is adjusting to the faster speed of play. (Applies both to keepers and field players.) That requires enough fitness and technique to keep up. Once you are at that level of play you can develop more tactically and mentally. But if you cannot adjust to the higher speed of play, you may get a look or a trial but you will be ineffective on the field and won't be selected to play at the higher level. Remember scouts say the top three things they look for in a player is "speed, speed, and speed."
Psychology and a great first touch are the most important parts of the game. Seriously, the psychology of your players is important, getting them to listen, do what you want exactly. and believe they can beat the opposition team with whatever tactics you want them to play. If you give instructions to you players can they follow it exactly? if something goes wrong can they fix it? will they keep an open dialouge with you the coach?
I was a scout for the A league I looked for player vision, quickness in a small space and first step explosive speed more then just speed, ball control and a good player ressume. That got you a try out with an A league team.
