No, it's mostly because Tinycore was designed around being as small as possible, it is compressed to the ground and has a few kernel features stripped down (which could potentially result in worse gaming performance and driver issues as well as hardware detection issues, in theory it could also do the opposite and massively boost the performance, I don't know, I haven't tried, I just have a hunch it might be unsuitable for gaming performance)

Tinycores purpose is to fit on as small a device as possible, you can game on it, I just said I would not recommend it (and I would not recommend it because if you're installing games, it won't be so tiny anymore and therefore it already defeats the purpose of the distro, and if the kernel is so heavily compressed I would be surprised if there is no hit on the driver performance for it, still, I might be wrong and maybe there is no performance hit, I haven't tested the theory, it might be the opposite and it could actually be faster, I know some BSD flavors were able to run Linux's native games faster than Linux itself by implementing a Linux compatiblity layer in it's kernel, tinycore might do something similar, performance is not the same across distributions because of different kernel versions and driver versions, and for example I know tinycore in the past could not run Steam when it was new to linux because libc6 was outdated on it, but if you can't run steam itself of course you're not gonna be trying to buy games on it, right?)

So my point wasn't that it's best to use a specific linux, if there was any I'd point towards Gentoo because it can be carefully customized to outperform all other linux distributions in any area the user chooses (this is because of how it is set up, and requires a LOT of user expertise i.e. is not some default setting so I am not recommending to actually use Gentoo here, the reason it can be customized so much is 1: Configuring the kernel is a part of the installation process, I know of no other distribution that does this and for amateurs this is an overwhelming task which they usually can't be responsible for, 2: Almost every program installed (Exceptions: Some proprietary programs, and video games, the steam runtimes too, but you can run games by manually installing dependencies instead of using the steam runtimes) is going to be compiled on your system for your system (you don't install programs like you do on other operating systems, by going through an installation, you install it pretty much the same way a programmer creates it, this process takes a lot of time btw) and as a result depending on how your compiler is configured you can have all installed programs specifically optimized and geared towards your system (this means that this installed program would probably not work on somebody elses system, for example if you optimize it for an intel i7 processor it might not work on a computer that uses an AMD processor) and of course configuring the compiler parameters is part of the installation as well and something that needs to be actively changed as well by the user depending on which application they are installing, now that is what you can call complicated. But if you do it all and you do it right, then in theory your Gentoo setup should be faster than any other setup as long as it's up to date.

But there are some Linux distributions aimed specifically at gaming, these include (but are not limited to) SteamOS (which has brought a lot of improvements to the Linux gaming arena as a whole, not just for itself, for example Valve pulled some strings and got nvidia to actively start updating their Linux drivers like their lives depended on it, this happened before SteamOS was officially announced by name and I was reaping the benefits of it already, this is because they wanted to set their steam machines up aimed at primarily using Nvidia graphics cards) there is also the Gentoo based Sabayon and Linux Console (which implies SteamOS wasn't the first distro with the idea of running as a console)

I do not however suggest you should use whatever distribution is best suited for gaming, I recommend you use the distribution that is best suited ]for you as a user. Mint offers easy access for people who are used to Windows 7/XP like user interfaces, Ubuntu offers in turn easy access for people who are used to OS X/Windows 8 environments. This is why the two are what is most commonly used. But for me neither was really right, I like to customize, I love to customize, I'm that type that spends hours in character creators if there are enough options in it (ELDER SCROLLS!!) so for me I wanted to find a distribution that offered me as much choice as possible. My favorite Desktop Environment currently is Enlightenment (version 17 or newer) and this desktop environment only comes installed by default on one distribution which is known as Bodhi, I hate Bodhi's default settings for it (theming, i didn't like the bodhi themes, but I liked Enlightenments default theme quite a lot!)

By definition this means I should use Bodhi because it's the only distro with the environment I want to use, but instead I opted to use a distribution like Arch Linux or Gentoo which offers me the freedom of choice to install and uninstall desktop environments as I please, when I get tired of one I can try another, what if I really always wanted to use something like Xmonad or AwesomeWM? what about Openbox? Maybe I just wanted XFCE all along!

So no, it's not use specific Linux instead of any Linux, but it is most commonly suggested to use Ubuntu because everyone "officially" supports it as the most widespread Linux distribution, this does not mean however that stuff that works on Ubuntu wont work on everything else, it just means it won't work on everything else UNLESS it is as up to date with its kernel and dependencies as Ubuntu is (which most distributions should be, if they're not theres normally a specific reason for it, for example in Debian's case they want to maintain elite levels of stability and thus only officially release LTS class kernels which use LTS repositories as well which means outdated software, this makes it highly ideal to use for servers for example.)

But there are general purpose distros and there are targeted distros, Ubuntu is aimed at general purpose, Mint is aimed at general purpose, Tails OS is aimed at internet anonimity, it doesn't even want to run if you don't run it from a livecd, you could game from it, but it would just be very unhandy because of how it is set up. Same with Tinycore, it's aimed at cramming an operating system into the smallest space possible (currently as low as 15MB if I recall correctly, even arch comes out of the box as like 2GB, and that one doesn't even ship with a desktop environment at all)

SInce we're on topic with Tinycore, one thing it (and also Slitaz which I previously named) does is something really special, it is designed to run from RAM alone (i.e. you do not need a hard drive to run it) basically if you install it, it will load all your data off your hdd/ssd onto your RAM, all your installed programs, everything, as a result it will perform lightning fast (SSDs are slow in comparison) but in return it just might take a bit longer to boot since it has to offload all the files on your hard drive to the RAM first before it can boot at lightspeed.