The problem is partly the definition of Antigen that you quote. It refers to “the body” leading you to assume it’s a specific body — yours. I'm sure there are better definitions, but just taking this one, I would modify to: “A substance that can be recognised as foreign and evoke an immune response in an organism.”
With this definition, which is actually how antigens are thought of, a particular antigen need not be antigenic in every organism to which it is presented. Those organisms or individuals for which the antigen appears as ‘self’ will not recognize it as foreign as they are ‘tolerant’ to it (e.g. by mechanisms which eliminate the cells capable of producing antibodies against the self antigen). But it is still referred to as an antigen.
So your understanding of the situation is correct, but that of the use of the terminology is not. Even if you belong to blood group A and therefore will not mount an immune response to the pink blobs in the picture when transfused with blood of group A, they are still referred to as antigens as they stimulate an immune response when transfused into a person of blood group B.
If you wished to talk about the fact that the A antigen on blood of type A does not provoke an immune response when transfused to persons with blood group A you could say “The A antigen on red cells is not immunogenic (or even antigenic) when transfused into persons of blood group A”.
Footnote on terminology
Scientific terminology allows us to describe things precisely. As our understanding increases, the terminology may need to evolve to allow us to make distinctions of which we were previously unaware. The word ‘antigen’ was coined in the late 19th century, before anything was known of the structure of antibodies, and was defined in terms of the immune response as that was what was observed. The definition evolved in some quarters to include the idea of binding to an antibody or T-cell (see e.g. Merriam-Webster definition).
However this extended definition raises the problem of the terminology to use if something binds to an antibody but does not provoke an immune response. Thus, the Glossary of the textbook Immunobiology (Janeway et al.) defines antigen as “Any molecule that can bind specifically to an antibody” and uses a different term, ‘immunogen’, for “Any molecule that can elicit an adaptive immune response on injection into a person or animal”. (Which explains my mention of ‘immunogenic’, as opposed to ‘antigenic’, above.)