- Games are a form of gambling
- Games are a form of marketing or promotion
- Games are a form of educational tools
- Games are a form of media
- Games are a form of hobby
Meanwhile, I doubt that any of these takes into account games made in-house for promotion or games included with educational products. I don't know whether poker chip suppliers are included (Toys? Probably adult entertainment). Are RPGs part of the books industry? Hence the impetus to create a new look at an industry that doesn't seem to officially exist.
When you start to sort through and follow links to 10,000 companies, you find yourself needing to classify them. I've got five categories, so far. A single company can belong to more than one category, though most belong to only one.
- Suppliers: produces parts or consulting to help others create games. For example: game designers, miniature casters , dice, paint, box, and casino suppliers, game consultants, printers, and so on. Suppliers help create OTHER people's games. If they only create supplies for their own games, they are not a supplier. 
- Publishers: creates games to sell, either public domain games or ones to which they have designed or acquired a license. They may use suppliers for nearly all aspects of producing the game. They may sell to both distributors or retailers. As a special note, publishers in this category must produce at least two distinctive games or game lines. Otherwise, they are single-game game companies.
- Single-Game Game Companies (aka sggc): Sggc's produce a single game or a single line of games (such as "X", "X Jr", and "X family edition"). These companies are of particular interest to me. Most create highly unoriginal games , and most don't last more than a year and a half. If they publish a second game that is not simply a reworking of their first game, they graduate to a full-fledged publisher. Promising to create a second game doesn't count; MOST of them promise to do that but never actually get the second game printed.
- Distributors: Distributors take OTHER people's games and sell them to retailers. Some distributors sell both to retailers and directly to the public. If they only distribute their own games, they are not a distributor.
- Retailers: Retailers sell OTHER people's games to the general public. If they only sell their own games, they are not retailers. Retailers may be web-only or brick-and-mortar, may sell only games, or may sell other things as well as games (such as a gift shop that sells a localized copy of Monopoly or a local artisan's chess board).
- Possibly separate game designers, miniature creators, or design consultant companies out from suppliers.
- Possibly distinguish between retailers who primarily sell games (like a game store) and retailers who primarily sell other goods (like a department store or a gift shop). Of course, what do I do with (for example) Mike's Games and Comics Shop?
 Miniature companies who provide rules are also considered publishers.
 But don't realize it.
 Update: I forgot one more: licensing. License holders and license brokers also make money off of games. I currently classify these as suppliers.