There’s still a well-defined answer to the question of what the digits mean, and indeed of what they mean as digits of pi; e.g., the hundred-billionth digit of pi is what you get by carrying out a pi-computing algorithm and looking at the hundred-billionth digit of its output. Anyway, no one is memorizing that many digits of pi.
[EDITED to add:] On the other hand, people certainly memorize enough digits of pi that, e.g., an error in the last digit they memorize would make a sub-Planck-length difference to the length of a (euclidean-planar) circle whose diameter is that of the observable universe. (Size of observable universe is tens of billions of light-years; a year is 3x10^7 seconds so that’s say 10^18 light-seconds; light travels at 3x10^8 m/s so that’s < 10^27m; I forget just how short the Planck length is but I’m pretty sure it’s > 10^-50m; so 80 digits should be enough, and even I have memorized that many digits of pi (and forgotten many of them again).
There’s still a well-defined answer to the question of what the digits mean, and indeed of what they mean as digits of pi; e.g., the hundred-billionth digit of pi is what you get by carrying out a pi-computing algorithm and looking at the hundred-billionth digit of its output. Anyway, no one is memorizing that many digits of pi.
[EDITED to add:] On the other hand, people certainly memorize enough digits of pi that, e.g., an error in the last digit they memorize would make a sub-Planck-length difference to the length of a (euclidean-planar) circle whose diameter is that of the observable universe. (Size of observable universe is tens of billions of light-years; a year is 3x10^7 seconds so that’s say 10^18 light-seconds; light travels at 3x10^8 m/s so that’s < 10^27m; I forget just how short the Planck length is but I’m pretty sure it’s > 10^-50m; so 80 digits should be enough, and even I have memorized that many digits of pi (and forgotten many of them again).