This is a common MySQL problem - specifying non-aggregate/non-aggregated-by columns in an aggregate query. Other flavours of SQL do not let you do this and will warn you.
When you do a query like yours, you are selecting non-aggregate columns in an aggregated group. Since many rows share the same genre, when you select Movie_Name
it picks one row at random from each group and displays that one, because there is no general algorithm to guess the row you want and return the values of that.
You might ask 'why does it pick randomly? It could pick the one that max(Rating) belongs to?' but what about other aggregate columns, like avg(Rating)? What row does it pick there? What if two rows have the same max, anyway? Therefore it cannot have an algorithm to pick a row.
To solve a problem like this, you have to restructure your query, something like:
select Movie_Name,
Rating,
Genre from movie_test mt
inner join movie_genre
where movie_test.Movie_ID = movie_genre.Movie_ID
and Rating = (select max(Rating) from movie_test mt2 where mt.Genre = mt2.Genre
group by Genre
limit 1
This will select the row with the rating being the same as the maximum rating for that genre, using a subquery.