This isn't an excuse for Intel and how they (sometimes poorly) handle issues that come up. And it is well known that many of these vulnerabilities are currently specific to Intel and how their subsystems are implemented, or only exist on Intel processors. But side-channel attacks are a nearly universal vulnerability.
SMT of which Hyper-Threading is an implementation of is used in many chips from many companies, AMD's Bulldozer, IBM's POWER, Sun/Oracle's Sparc, etc.
These exploits are not a monolithic process, but many techniques chained together to get most of these exploits to work, and this common knowledgebase which has been refined by the researches will most certainly be recycled and reused on other processors.
If anything, the "capture 90% of the market." by Intel as you put it only ensures that these problems will usually be discovered on their processor's first.
If as much effort was put towards other cpus as it is towards Intel, you would see significant performance hits as well with them.