Two things come to mind: you don't need the apostrophes, $game{board}{proposedworduser} will interpolate just fine. Another thing is that with a temporary variable, you can factor out the $game{'board'} derefs.

my $g = $game{'board'};
$g{stat} = "$playerin submits $g{proposedworduser} $g{proposedscore} p
+oints";
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Now, if those hash keys weren't so long, you'd be in business :)

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update: that should probably read  $g->{stat}, but you knew that already...