But they would be arranged in various specific ways. Then, so long as the polymers can reproduce, the relative ease and fidelity with which differing sequence can and do reproduce represents meaningful information.
Scrabble tiles can't and don't encode structural information the way a biopolymer does. We can READ the scrabble tiles, and determine if they are words or gibberish, but they are structurally the same -- just wooden tiles -- either way.
The scrabble tiles only have primary structure (the simple sequence of subunits) and all the information is soley in that sequence, only in the primary structure.
All biopolymers also have secondary structure (local hydrogen bonding) and tertiary structure (3-D molecular shape). Even randomly generated primary structures will have different secondary and tertiary structures, and inevitably some secondary and tertiary structures (and thereby some primary structures) will reproduce better than others. Thus there is meaning ("how well do I reproduce myself?") even to random primary structures (random sequences) provided only that they do reproduce.
Scrabble tiles just don't work like that.
... so long as the polymers can reproduce ...Reproduction is only possible with much highly specified biological information being in place. We are discussing the origin of that information, so we can't use processes dependent upon its existence to explain its origin.
--Stultis