i live with two INTPs. your writing sounds very much like the way they reason, too. it's very Ti-based. more "dry" sounding to me than "fuzzy" Fi.
liking sports is not very INTP stereotypical but there is no reason why you cannot be an INTP who loves sports. i am an ENFP who loves the phyiscal aspects of driving and that supposedly goes against my type.
as someone explained before i choose I over E not because of your mentioning that you are not very social, but rather the way you describe not being very social.
also, Ti can really come off as J in simple tests - INTPs are often meticulous with their things, etc. - so it doesn't throw me much if you've tested as INTJ previously.