You clearly don't understand. No one is saying that Sony 1st party games don't help sell a lot consoles. What was being said is that if you took all the major 3rd party games away, PlayStation would sell less then it currently sells and that would have a negative effect on how much 1st party titles can sell.
The reason Sony sells better than Xbox is mostly down to Sony having much better 1st party support. It is the combination of 1st and 3rd party that makes Sony consoles sell so well.
First party is one factor, but Sony also went to market earlier, captured the userbase and expanded the entire medium. There's a lot to be said being the first or a pioneer in any industry. Xbox had a similar formula but 7 years later to market- by that stage PlayStation was already the established market leader.
Yes, it's the 'play everything' approach that works for Sony- 80% third parties 20% first party by revenue. While the complete reverse is true of Nintendo- FY 18' had a 80% first party 20% third party revenue split. In the end though Sony tends to sell far, far more software overall. The PS4 currently has sold more total software than the Wii, Wii U and Switch combined.
There's also the history and entire approach to first party development- the more you look at it the more the comparison just seems like Apples to Oranges.