Why are non-printable ASCII characters actually printable?
ascii
Solution
Most of the original set of ASCII control characters are no longer useful, so many different vendors have recycled them as additional graphic characters, often dingbats as in your table. However, all such assignments are nonstandard, and usually incompatible with each other. If you can, it's better to use the official Unicode codepoints for these characters. (Similar things have been done with the additional block of control characters in the high half of the ISO 8859.x standards, which were already obsolete at the time they were specified. Again, use the official Unicode codepoints.)
The tiny print at the bottom of your table appears to say "Copyright 1982 Leading Edge Computer Products, Inc." That company was an early maker of IBM PC clones, and this is presumably their custom ASCII extension. You should only pay attention to the assignments for 000-031 and 127 in this table if you're writing software to convert files produced on those specific computers to a more modern format.
Problem
Characters, that are not alphanumeric or punctuation are termed not printable: Codes 20hex to 7Ehex, known as the printable characters So why is e.g. 005 representable (and represented by clubs)?