The win sees Glasgow stay top of the URC table with Stormers four points behind in second place.
"It's the way we train and the way we try to develop the game," head coach Franco Smith told Premier Sports when asked about his side's attacking intent.
"I think the game is going that way. If you look at the Six Nations, there were a lot of tries scored. It's maybe what's demanded of the game now.
"That is the ingredient that brings enthusiasm to club rugby as well.
"We were going to try and score as many tries as possible, but I didn't think we would get to that many. I thought we played really well. I was really proud of the boys."
Glasgow struck four times in a blistering eight-minute spell, taking full advantage of two Leinster yellow cards to build a 26-12 lead by half-time. They then put the result beyond doubt with two more tries in the final quarter.
Scrum-half George Horne scored twice and added four conversions, finishing with an 18-point haul.
Speaking to Premier Sports after the match, he shed more light on the team's attacking approach.
"Franco is so good at keeping it simple for us," he said.
"Usually, it's be brave and move the ball. You saw that in the first half. We were moving Leinster around and they had to make 130 odd tackles, I think."
Horne returned straight to the Glasgow starting line-up despite playing in all five of Scotland's Six Nations fixtures.
"I couldn't go a week without this place!" he said.
"Coming back to play Leinster makes it pretty special. They have been the best team in the league for a few years now.
"It was good. It makes Monday morning a lot easier when you come in after a win like that."