There are a variety of measures, or counter-measures, that you can employ. Some are technology-based, some come at a financial cost, some require the right level of cultural and institutional authority to implement.
The least expensive, and tech-free alternative is to set rules with consequences. When the instructor is lecturing the students are expected to be listening. Listening is done with the mouth closed and the ears open and eyes on the instructor, not the "game". During "lab" time on-topic discussion is acceptable while discussion of current events (current pairings, etc.) is not considered on-topic.
If the students are expected to use paper for notes, rather than the computers, during the lectures, you can also require that they remain powered down until the "lab" portion of the class begins. Once they are working on the computer, the rules can say "No Games" and that can be explained to include both the Windows per-installed games, and online games of any variety.
Still non-tech, and possibly within a limited budget is the installation of mirrors. One or two strategically placed bubble mirrors can allow you to "see" the monitors even when you are on the other side of the row from them. Granted, the image in the mirror won't allow you to read their screens, or probably even know what program they have open. Even with the limited quality of view they offer you should be able to distinguish between an IDE and a video game, or a music video, etc. Even the difference between a web page being used for research and a chat/IM window is probably distinguishable that way. The version that hangs on a chain should be install able in almost any classroom, and without much effort from maintenance, possibly even on your own.
If the room's shape and the outlet distribution allows it, you can consider the tables mentioned in another answer. Even the pre-computer versions of the half-hex tables can accommodate a trio of flat-panel monitors if you can have the CPUs on the floor. There is the trade-off of loosing writing space for the keyboard, but if they take paper notes during lectures, with the computers remaining off, the keyboard can be moved out of the way.
The cost for the tables depends on what's currently collecting dust in the warehouse and what is purchased new.
Adding technology to the mix, there are other measures that can be pursued. First off is the uninstallation of all the games that are bundled with Windows. There seems to be no real reason to have them on computers that students are supposed to be using for schoolwork. It might cost the IT Dept. some time, but it won't cost them anything else.
Depending on the school's policies, it's also possible to restrict the sites that are reachable from the school's network. This shouldn't require any new software for the system, just the configuring of what's already there. Most of the popular games for your students are likely to be from a highly limited set of domains, domains which server no other purpose. Blocking traffic to those few IP addresses can be handled by even a simple home router, whatever is in use at your school ought to be capable of the same. If your school is setup with each room on its own VLAN then they could configure your lab's network to block those sites while allowing them for the rest of the school, and for the WiFi access from student devices. I don't think there's a legitimate need for access to such sites from the school's network at all, but the school policy might not allow a global blocking of such sites.
The most expensive, and probably the most complicated to maintain, is to install some form of "parental control" software on each student computer. (Removing, or disabling, unwanted software at the same time can't hurt, or course.) I have no recommendations for which one to use as I've never bothered with any of them. It's likely that the cost and licensing of them will have a larger impact on choice than features in any case. Institutional bureaucracies tend to move in that direction, even when it means getting something that does half of the task only half as well as something else would.
Still, no matter which measures, at whatever costs and technology level, are used, they only make sense when used to enforce an existing rule. If there is no rule against playing games during lab time, blocking game sites is not appropriate. That realization just returns the subject back to the top of the list.
With the understanding that there are some rules to follow, which are explained to the students in the beginning, you can still attempt to keep things "light" for their first real exposure to CS. If the class is for programming, you can work towards developing a game as part of the progression of the class. Obviously it will be a simple game compared to what they like to play. Being part of the team that makes it, however, can add the excitement lacking from the game itself. I suspect that even today's kids know what tic-tac-toe is, and its rules. Making a quick version of that early in the course can cover a lot of the language basics without needing major investment into complex libraries and programming. If developed early enough in the course, it ought to fuel their fire for making a "better" game during the remainder of the course.
Whether the end is a game, or something else, the sooner you get the students where they have "made" something which does something and they can see the results of their work, the better your chance is of getting them engaged and invested in the material. I believe that is one reason web design classes do so well - the view-able web page, no matter how "basic," is so easy and fast to create that there's nearly instant engagement of the students.
One final suggestion, to encourage them to see computers as a "game" of its own, a game where the computer is made to imitate what people can do, while giving them a bit of computer history as well, you can show the movie The Imitation Game about Alan Turing and breaking the German Enigma machine's code.