Myers-Briggs as it is right now is just a measure, or rather an attempt to measure, personality traits. It's simply a categorization based on (typically self-reported) observations about a person's preferences and such, so it doesn't really make sense to say that these preferences are because of your Myers-Briggs personality type. You may be able to predict other preferences based on your personality type, and that's in fact the main point of the classification, but that's different from saying it's because of your personality type that you have these preferences.

Myers-Briggs says nothing about cause, it doesn't care whether personality is random or determined by genetics or something else entirely (what determines personality still is not fully understood and probably won't be for a long time, so if you want a concrete answer to that you're out of luck), it's simply a classification. Having a certain Myers-Briggs personality type certainly won't prevent you from enjoying games like Monster Hunter, the most it can say is something like "based on your answers to the personality test it would be most consistent if you didn't like Monster Hunter." If you in fact don't like Monster Hunter, the prediction was correct, if you do, then it wasn't correct, which is also perfectly fine because people don't fit neatly into discrete categories no matter how much they try to create such categories. And if your preferences for many things are consistently inconsistent with your Myers-Briggs personality, it probably means you were categorized inaccurately.

Whether you actually do enjoy Monster Hunter will be based on observable factors like "do you like weighty combat," or "do you like gameplay structured around repetition rather than progression through a story." As I said before, as far as I know we can't yet reliably link one's answers to these questions to any objectively measurable trait in the human body.

You could think of it a bit like classifying elements in the periodic table. When Mendeleev created his periodic table he arranged the columns according to elements sharing similar properties, such as violent reactions with water. Using his table he was able to predict the properties of several elements that had not yet been discovered. But it was not until much later that it was understood why, on an atomic/quantum level, the alkali metals were more reactive and the noble gases were inert.

tl;dr: Myers-Briggs is a classification of what we can observe, that can be extrapolated to make predictions, but it does not say anything, nor do we know a whole lot, about what the underlying causes of such tendencies are.