As an ex-arcade guy who now works in the slot machine business, I would like to point out the statement that "Bally leads the market" is incorrect. They are sort of a middling player at this point.
As far as American marketshare for "class 3" (class 3 being games that you would find in Vegas) goes:
IGT is the market leader. That had what I would call a near-monopoly at one point during the 1990s. Probably close to 95% of all gaming (ahem) machines bore an IGT logo, mostly due to patents involving "virtual reels," which have recently expired. However, their reluctance to embrace video slots caught up with them. They picked up the pieces eventually, but due to the fact that the five-reel video format has no patent protection (and conveniently gets around the pesky virtual reel patents), it enabled many other companies to get into the business. Still, it seems that IGT probably still holds anywhere between 50% - 70% of the casino floor positions.
Next up would be Aristocrat and Williams (now called WMS).
Aristocrat is an Australian-born company that is known as really bringing the 5 reel video format to the forefront. However, due to some issues with the core management at the time (early 90's), they were never allowed licenses to operate and sell their games in the larger casino markets, such as Nevada. Which meant that they were only selling games into the Native American market. (They did fix their management issues, and as such, now have licenses to operate everywhere.)
Which brings us to WMS. Desperate to break into the market, but with licenses everywhere, they copied the Aristocrat format and were able to sell it into Nevada and Atlantic City. So, they wound up being the company that "mainstreamed" the format (while most of the other players in the industry dismissed the video slot craze as a fad). They were pretty much poised to take over the casino, except for a bunch of software bugs that slowed them down A LOT. This allowed everyone else to play catch up.
Bally sort of fits between the top three and the group of "second tier" players, which at this point, would include Atronic, Konami, and Progressive. AC Coin probably goes in this group, too, but they are a rather unusual outfit, as they are more of a retro-fit type company (they develop top box bonus games on top of pre-existing games), as opposed to a pure developer.
Multimedia is a huge player in "Class 2" (Bingo-based Indian Reservation Gaming and networked lottery systems), I'm glad to see them getting some amount of mention. Usually, you only read interviews from the "Vegas guys."