If you can
1. make a dedicated office space, which helps you mentally flip the switch when you sit down. In this case, move the gaming laptop away. Keep only the work laptop, maybe even clean it up of any distractions, unrelated files and apps and turn Wi-Fi off on it should intenet not be needed to do the job.
2. establish a routine and habit. This will take weeks to months to figure out. If you find yourself drifting off at certain times, put in breaks and allow yourself to do something else for a bit, but - impotantly - don't do it in the office space you made. Get up, ideally into a different room or take a walk outside. Never allow yourself to do anything unrelated to the job at the "office". If you can't concentate, get up immediately and leave until you can focus again.
3. measure your success in hours or tasks but not both or you'll beat yourself up before you reach the breakthrough. This varies by personality but I found I do better when I set myself concrete goals for the work day. I can start as late as I want, take breaks as often as I want, and finish as early as long as the task I set myself for the day is done. Some do well sticking to a hard schedule of working specific hours at regular times each day and if you go that way it's important that to start with you consider it a good day when you just manage to stick to the schedule. I ask myself what would I need to get done today to consider it a productive day, and if I achieve that I feel accomplished, and anything done on top of that is extra gravy. This approach also allows you to slowly increase what you demand of yourself over time as you get comfortable with working alone, without giving you that feeling that you're constantly failing in those early getting-used-to-it days.