Gaming will demand maximum performance from your Mac, but it won't damage it. As its temperature limit is approached the system will throttle the CPU so as not to exceed it. If that doesn't reduce its thermal load the Mac will simply shut down.
I still think 200°F is too high but I'm not much of a gamer and have difficulty getting my MBPs to get anywhere near that temperature, but if Apple says they examined yours and determined it to be OK then I'm inclined to believe it's OK.
It's normal for the case to feel warm, but not excessively hot. Don't impede the Mac's heat dissipation by using cases or "skins" because the entire aluminum housing serves as a heat sink.
If you are interested in extracting meaningful data, consider the following. While the game is running and the MBP is hot enter the following line in Terminal (triple-click to select the entire line, then copy and paste it into the Terminal window):
clear; printf '\e[3J'; P='pmset' S='\n####' Q=(Thermal Load Events Assertions Preemptions) R=(therm sysload 2 3 4) ; printf $S\ ${Q[0]}'\n'; $P -g ${R[0]} ; printf $S\ ${Q[1]}'\n'; $P -g ${R[1]} | tail -n 4 2>&1
Select All that Terminal window's contents, copy and paste the results in a reply. It may or may not reveal anything noteworthy.
Delete or obscure any information you might consider personal, such as your Mac's name or your user name.