Is SEO aimed at Google only or at ALL search engines?

Based on traffic share mainly Google is Focused but you cant ignore other's also , 

As Husain mention its based on project to project Like if you work for Chinese client you cant ignore Baidu , for Latin America Market Google Hold upto90% search traffic , i not remember exactly but on some parts Yahoo hold good numbers so there is no permanent formula but overall Google win

No, SEO is aimed to all search engines, however Google is the most difficult search engine to conquer, that’s why every SEO effort done to get higher SERPs in Google automatically enhance the SERPs of other search engines such as Yahoo, Bing, Ask and etc.  On contrary, if we just struggle and finally rank on1st page for Yahoo (or etc.) it doesn't assures that we will have also got1st page ranking in Google,

If Google is difficult to win, then why do we struggle for Google?

We mainly focus on Google for our organic search results, because Google sends around70% of all the search traffic for any search query. 

As we all know that SEO stand for Search Engine Optimization and it's aimed to be for all search engines but as we use google more often than other search engines se we related the SEO to google and also we use the SEO to generat organic traffic to websites from appearing in search results. So I believe that fully optimized website will generate more organic traffic with using the right SEO campaign.

Basically SEO is for all search engines however depending the country we live in focus more on the primary search engines and Google being the most commonly used search engine in many countries, so we focus more on Google.

Basis my experience if we can optimize our website for Google we are very likely to rank for others as well since google has the most complex algorithms.

Search Engine Optimization, it's not called GSEO :-), i mean Google search engine optimization.

SEO is mainly aimed at Google due to the highest market share in Search Engines, over60%.