Yet no one who is still taken seriously says wealth is zero sum.

If your point is holds true, and we are at saturation for attention, then if radio contact was made with an alien probe tomorrow, the amount of attention people are paying to the news would not change, but merely more of it would be devoted to your discovery.

That's crap -- the overall amount of attention people are paying to news would actually increase. Other stories would indeed be overshadowed (hence your confusion in thinking attention is zero-sum) but the total amount of attention would not be constant. Instead, it would crest like flood-level waters moving downriver.

The total amount of attention being paid to news is not constant.

This is an interesting rhetorical trick: present a slice of the pie as the entire pie, so that when the size of that slice grows, you can claim that the pie was actually infinite to begin with! Nice.

The difference between wealth and attention (as your carefully selected example shows that you actually already know...) is that you can create wealth without taking decreasing anyone else's wealth. Three people on a desert island can become wealthier all at once. However, there are only a certain number of things anyone can "pay attention to" at once, because paying attention to something necessarily means decreasing attention to something else.

the total amount of attention would not be constant.

If you limit yourself only to the slice of total attention you have called "news", then you'd be right. But most of the time I'm paying attention to things other than news. Some of those other things include celebrities, even.

hence your confusion

I believe you misspelled "conclusion", here. :) Confusion only arises if you start from the assumption that attention paid to online games, programming, blogs, texting someone, getting a drink, or going for a drive, isn't attention at all, because it's not narrowly focused on news.