Your issue likely lies somewhere within wp-config.php. You should not need to run any install if your tables already exist, the wp-admin/install.php is only used when no tables are detected with the settings in wp-config.php.
Going through parameter by parameter, I’ll give you some idea of what everything is.
DB_NAME is the name of the database that WordPress should access. Make sure this is set to the database that you want to use.
DB_USER and DB_PASSWORD are the login credentials. As you are not getting a database connection error, these are likely correct.
DB_HOST is how WordPress is to connect to the database. Again, no database error likely means this is fine.
Don’t worry about DB_CHARSET and DB_COLLATE unless you have specific reasons to change them, it’s just database settings.
The last thing you need to worry about is $table_prefix. Based on the comments, my best guess is that this is your issue. If you look at the tables you imported, they should all be named something like wp_posts, wp_options, etc. Whatever the common thread between them is is what you need to set as the prefix. Make sure you set it EXACTLY the same, including the _ if it’s on there. WordPress doesn’t add anything to this, it just concatenates the table name onto the end of it.