Well for starters it is clearly hyperbole. There is no way Yahoo particularly wanted to be part of everyones porn surfing for example - Tumblr notwithstanding. And you'd find plenty of other niches where Yahoo made no attempt whatsoever to enter.
And outside of investment in Alibaba, their involvement in online shopping was marginal. In fact, Yahoo's premium services was always marginal across the board - I spent years trying to push product teams to find services they could potentially charge for in Europe, and from what I can tell my replacements had no luck in that respect either.
Instead Yahoo actually divested a number of services in that respect. Yahoo! Personals was sold to Match.com, and while it may have been co-branded for a while, that's long since lapsed in most markets.
So either Yahoo dramatically failed to follow this up in any reasonable way, or the actual intent was a lot narrower. Or both.
But what does "be a part of" even mean? Have an ad on the page? Be recognised by the user as providing the service? Providing content? Provide the tech? It really says nothing. It doesn't say anything about the purpose either. Is it to sell more ads? To grow the brand? To drive people to premium services?
It's a non-statement.
To me it's a statement that's basically carte blanche for whatever management happens to want right now, but it's certainly not providing focus.
And while I would interpret it as directed towards media, I suspect it did nothing to e.g. clarify to the company whether Yahoo was a media company or a tech company. Maybe intentionally, because there were a lot of people in engineering when I was there who did not want to accept that what mattered to Yahoo was connecting eyeballs to content, and that.