A typeface impacts my perception of content by the manner in which the typeface fits into the 1) layout and 2) the application. A news or information website, for example, will reasonably make use of a typeface which is easy to read and presents information with urgency and importance.
If the same website were to make use of a typeface which adds “style” or pizazz to the content, it wouldn’t communicate the same urgency or importance. A “Western-style” typeface, for example, only suits certain situations, such as stylistic, period-style advertisements. A typeface which is in the style of one of Sagmeister’s creations would fit grunge music or goth metal websites.
However, if a website were tailored toward the selling of certain products, then the typefaces would most reasonably fit the sorts of products being sold. If I go to Apple.com, select a word on the website, right-click to select “Inspect Element” in Chrome, and de-select “Lucida Grande” from the list of CSS attributes, the resulting serif-ed typeface simply wouldn’t fit the graphic theme of the rest of the page, which calls for smooth but “faint” and “light” tips and flourishes, as most of the graphics of the website communicate.
So the choice of certain typefaces are more purposed toward being part of the website’s graphic layout. Compare with a news or information website which is purposed toward presenting information, not products of any particular aesthetic. Such typefaces do their job when they immerse the user into the presentation’s theme and core topic, and do their job when they elicit a reaction as desired by the website’s owners.