The "telephone game" picture of Scripture is almost the opposite of how the manuscripts actually work.
The New Testament has unrivaled manuscript support
We have over 5,800 Greek New Testament manuscripts, plus more than 10,000 in Latin and thousands more in other languages. The earliest fragment, the John Rylands p52, dates to within decades of the autograph. By comparison, the average classical text survives in fewer than 20 manuscripts, the earliest hundreds of years removed. As Daniel Wallace has shown, this embarrassing wealth of evidence is the opposite of obscurity.
Variants exist but do not threaten the message
Critics like Bart Ehrman quote the figure of "400,000 variants" — but most are spelling differences or word-order changes, and no orthodox doctrine depends on any disputed passage. The text is not unstable; it is precisely because we have so many manuscripts that we can identify any deviation.
The Old Testament's transmission was also faithful
The Dead Sea Scrolls (1947) gave us copies of Old Testament books a thousand years older than what we previously had. The Great Isaiah Scroll matched the Masoretic text we already used almost word for word, with the differences being orthographic, not doctrinal.
For Orthodox Christians: Scripture is read within the Tradition that produced it
The Church that wrote, canonized, and copied the Scriptures also taught and preserved their meaning. The reliability of the text is not separate from the reliability of the apostolic Tradition that handed it down.