Putting creatures into play in alternative ways to summoning them
Cards like Quicksilver Amulet and Sneak Attack provide an alternative way to put creature cards into play, instead of casting them as normal. This has the following differences to casting them as normal:


Cards put into play this way are never on the stack; only the ability that puts them there is
The creature card will never be considered cast, and never be considered a spell
The controller of the ability doesn't have to announce the creature card until the ability resolves (at which point it can't be countered anymore). They don't even have to put a creature card on the battlefield at all if the ability resolves.


At the time you activate the ability of one of those cards, no creature card is involved at all. If a player chooses to Stifle the ability, it will be countered. Emrakul, the Aeons Torn's ability does not apply, because not only is it not a spell - it isn't involved in the situation in any shape or form until the ability resolves and the controller chooses a creature card to put into play.

Likewise, a triggered ability that triggers when a creature is cast only triggers when that creature is put on the stack as a spell (note how this is made abundantly clear by both of Emrakul's abilities referring specifically to spell). Using one of the cards in question, this never happens, so the controller will never get the benefits of a cast trigger by simply putting the creature into play.