As far as finding games on jinteki.net is concerned, you might try the Stimhack Cache Refresh tournament which you can find Here.
To answer your question, I think alternate formats are less popular online because everyone has access to all the cards, so there’s no real reason to place artificial limitations on themselves. After all, one of the main arguments in favor of alternate (i.e. limited) formats is to level the playing field for players who have smaller physical collections.
I don’t want to over-generalize, but I also find that the vast majority of players prefer the experience of the standard MWL vs. Cache Refresh or non-official formats simply because it offers the full breadth of strategies. There are a few major gaps in the CR card pool that reduce the effectiveness of some archetypes and essentially remove others. For example, without Hard-Hitting News or Midseason Replacements in the card pool, Tag n’ Bag seems almost impossible. If you’re the type of player who prefers to play those types of decks, it may feel like the format has very little to offer.