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The big difference between Nintendo's amiibo and other toys-to-life games is that those other series were basically 1-to-1 matches with specific releases. Every year, Activision would release one new Skylander game along with new figures. If one title did badly, that was it.
In contrast, Nintendo supported the heck out of amiibo. In 2015 alone, which was not a good year for Nintendo, there was at least some read-only support for amiibo in a dozen or so games, even though only a couple were amiibo-centric (Mario Party 10 and Amiibo Festival). Nintendo released twice as many amiibo-supporting games in 2015 as Activision released Skylander titles ever.
Also note that amiibo are all reasonably affordable figures of characters people already want merchandise of, something not necessarily the case with Skylanders. And there is also forwards compatibility; the upcoming Legend of Zelda: Echoes of Wisdom is compatible with amiibo released as far back as 2014's Smash for Wii U set.
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IMO, if a company wanted to get started in the toys-to-life business, they would need to release a fairly steady number of games per year, have rights to characters that would sell merchandise anyway, and would need a good enough reputation regarding not giving up shortly on projects. IMO, none of the big Western publishers meet that criteria; they often rely on games that don't have marketable characters, have poor reputations among the faithful collectors that sell half of these things, or simply don't release that many new products per year.
Disney could have done this with their Disney Infinity line, provided they chose to continue developing and publishing games that could support their figures. But Disney was already looking for the Exit to the games industry when they jumped on board, so of course it didn't last.
