There are two distinct conditions you need to be aware of
CONDITION #1 : Fragmentation
It is obvious the table has experienced lots of INSERTs, UPDATEs, and DELETEs (or non-SELECT DML). Even loading data sorted by PRIMARY KEY order will make index pages lopsided, at least 45% sparse.
I have posts about this phenomenon before
Thus, data pages shrinking from 8733835264 (8.13G) to 601882624 (574M) and shrinking index pages from 4875419648 (4.54G) to (~443M) is not alarming. This will improve read performance.
CONDITION #2 : InnoDB Row Count
InnoDB is notorious for INFORMATION_SCHEMA.TABLES having spurious counts. MyISAM tables give accurate row counts in the table_rows column of INFORMATION_SCHEMA.TABLES.
InnoDB likes to do dives into the index pages in order to guess the number the rows in the table.
I have discussed this feature before as well
If you want an accurate count of an InnoDB table, you must bite the bullet and run
SELECT COUNT(1) FROM calls_old;
which will produce the same count every time.
Running this:
SELECT table_rows FROM information_schema.tables
WHERE table_name = 'calls_old';
never gives you the same value each time.
In fact, if you run
SHOW INDEXES FROM calls_old;
look at the cardinality column. It will produce different numbers each time. You would have to lock it down by setting innodb_stats_on_metadata to 0. Even if you did that, the stats would become stale over time through normal non-SELECT DML just like a MyISAM table. Running ANALYZE TABLE calls_old with innodb_stats_on_metadata set to 0 will fix the index statistics.
Having innodb_stats_on_metadata remain at 1 will make ANALYZE TABLE calls_old completely useless. (See my post From where does the MySQL Query Optimizer read index statistics?).
Since the table is called calls_old, I can surmise that you do not need to adjust any other options since it may be an archive table as the name suggests.
EPILOGUE
The value of Avg_row_length is a good indicator that you should defragment the table. When you see an InnoDB table growing that much, you could just run
ALTER TABLE calls_old ENGINE=InnoDB;
to shrink that table.
Thus, the behavior you are seeing is driven by the two conditions I just discussed.
SUGGESTION
If you want to verify the contents, you should these two queries:
SELECT COUNT(1) FROM calls_old;
CHECKSUM TABLE calls_old;
before and after dumping/importing.