It currently is under Beta development which means that the game works... but still has some things that need improvement or bugs.
Beta keys (which are given by Blizzard) allow you to play the Beta version of the game (playing before release).
You should ask someone if they still have a beta key left.
It seems like blizzard gave everyone 5 keys if they joined... so those who got those keys also have 5 for themselves.
Mine have been given already so I have none left for you.
But there should at least be someone that has it.
Anyway, the game is a simple MOBA game (AoS) with different map styles.
In most maps, you collect things to spawn something that will help you destroy the enemy core (enemy base).
However, the gameplay itself is very different from DotA2 or LoL.
First of all, you dont have items... which is the only thing you would use gold for.
So gold is removed!
Also, XP is shared 100% so your level is the exact same as your teammates.
These two together actually remove individual gameplay from the game.
Which sounds great but actually is not.
Also, you have a lot of fountains which regenerate your health and mana in every lane just behind your turrets.
This actually makes recalling almost useless. (except if you are almost dead and you just activated the fountain regeneration)
Also there is nothing like runes or masteries or anything else that affects gameplay from outside of the match.
(This will only be for LoL players.)
Also, leveling abilities is done automatically... in fact, there are no levels of abilities.
There are a few other things that changed the gameplay.
In trade for items, there are talents.
Talents are unique abilities that can be learned at specific levels.
Each level has its own talents which you can choose from.
At level 1, 4, 7, 10, 13, 16 and 20 you can learn a new talent.
Each hero has his own talent tree.
Talents give a passive bonus to your hero by either increasing effects of your base abilities or giving you a new ability.
Some talents are castable for example the talent at level 10 will be your ultimate ability.
Just search on the wiki to find a few talents and you will find out how they affect your spells.
Another thing is mounts.
When you are out of combat, you can channel your mount, which grant you bonus movement speed until you enter combat or cast an ability.
Buildings have ammo which means that your turrets and forts will not always be able to attack enemies.
Buildings are also placed differently.
At the far end of each lane, there is a gate with walls and turrets.
Turrets deal damage, walls are pathing blockers and a gate is a pathing blocker for enemies.
Behind it is another turret and a fort (a stronger type of turret) together with a fountain which can be activated by every player individually to regenerate a portion of their health and mana over time.
All fountains will have a shared 100 seconds cooldown for each player.
I think that this will be most of the big changes between existing MOBAs and HotS.