To fix it, edit bin/kafka-rest-run-class and add:
if [ "x$LOG_DIR" = "x" ]; then
LOG_DIR="$base_dir/logs"
fi
just before
if [[ -n $LOG_DIR ]]; then
[[ -d $LOG_DIR ]] || mkdir -p "$LOG_DIR"
KAFKAREST_LOG4J_OPTS="-Dkafka-rest.log.dir=$LOG_DIR ${KAFKAREST_LOG4J_OPTS}"
fi