A 2-in-1 in that price range will have a low end CPU (Atom series) and while it will likely be able to play TF2 and CSGO, you will likely only get mediocre performance.
Within your $300 to $400 budget, the best laptop you can get is the following 15.6" laptop with a Core i3-7100u and Intel HD 620 integrated graphics core for $350. It also has a 1080p screen, but you may want to play games at 1366x768 or 1600x900 resolution for better performance.
https://www.amazon.com/Acer-E5-575-33BM-15-6-Inch-Notebook-Generation/dp/B01K1IO3QW/ref=sr_1_3?ie=UTF8&qid=1505784519&sr=8-3&keywords=i3-7100u
For $413 you can get the following 17.3" HP laptop with a Core i5-7200u and Intel HD 620. The Core i5-7200u basically has higher clockspeed than the i3-7100u. It only has a 1600x900 resolution screen.
https://www.amazon.com/HP-Flagship-i5-7200U-2-50GHz-Windows/dp/B01MQZ1FS7/ref=sr_1_5?ie=UTF8&qid=1505783485&sr=8-5&keywords=i5-7200u
For $479 (above your budget), you can buy the following 15.6" HP laptop with a Core i5-7200u and Intel HD 620. It only has a 1366x768 resolution screen, but it is a touchscreen if that matters to you.
https://www.amazon.com/HP-Touchscreen-Backlight-Flagship-i5-7200U/dp/B06Y6RK3S9/ref=sr_1_12?ie=UTF8&qid=1505783485&sr=8-12&keywords=i5-7200u