It's because there are a ton of Ruby implementations. MRI is the name for the official one that Matz works on.
If he said "Ruby's method caches," he would be wrong, this is about details of MRI specifically, and not, say, JRuby or Rubinius.
Given how much hackers love TLAs, and that there are what, 2600 of them, it's inevitable that there will be some amount of namespace clash. Ruby people reading a Ruby blog post aren't going to be confused about it, and while others may have momentary confusion, a few seconds later it's pretty clear what's being discussed.
Terms of Art are hard.
I think a good guideline for choosing an acronym is how many hits it already has on google. MRI: 73,800,000
If I told my parents I worked in Ruby all day they'd think I started a career in precious gem mining, who cares? "Those who know what it is will know..." are exactly 100% of the people that care about Matz's Ruby Interpreter and therefore this article.
Is it just me or is that a bit of an odd name? For me when I see MRI I think Magnetic Resonance Imagining, but is that just because of my field?