Passing and dribbling are key things that you can do on the pitch to take the ball further away from your goal even if you don't score, something that makes it harder for the other team to score, which finally helps you achieve that "score more than the opposition" fundamental you rightly mention.
You pass the ball because your rival can't score without touching the ball
You driblle forward 90% of the time, and the better you are at dribbling, more players will have to defend you, making the enemy attack weaker
As you get better at both things, you go from aimlessly passing the ball around between CB's and Midfield (what you call LVG school) with the danger it takes, to do it between midfielders and, best case scenario (Pep's Barça for example) between midfielders and forwards, demanding of the other team to bring extra defenders and to have 70 metres of space between where they recover the ball and scoring and with a limited amount of attacking players.
And that role is the key thing why we, the Messi-band, and many others believe he's better than Ronaldo, titles and seasons are decided on how good that part of the team is, you need guys like Leo, Iniesta, Xavi, Modric, Kroos, Silva, KDB, Pirlo, Pjanic, James, Thiago, Hazard, Verratti and so on to have some kind of consistency in your results at the long term, you can try to blow past midfield like Klopp does, you can taste success that way too, and maybe if you put Ronaldo in this Liverpool side he'd still score for fun, but there's a reason why teams with great players at 4,8 and 10 positions are the ones touted as favourites for everything from September to April.
Scoring is obviusly a needed skill, and that also affects the game in many ways even if you don't actually score but remanin a threat for the other team, but it's just the ceiling of the house.