Ok, a little run down. There might be minor spoilers as this is all comic book origin stuffs
Yes 'Arrow' is Green Arrow, Oliver Queen is Green Arrow in DC and their stories are ALMOST identical. In the comics things were slightly different, Oliver's parents died via a tiger on a hunting trip orphaning Oliver. He was still a billionaire in the comics and still became the Green Arrow after being stranded on an island and fighting to survive. The circumstances of the island are completely different and there was no Deathstroke to teach him how to be awesome. Speedy (his sister's nickname in the show) was actually a teenage boy, Roy Harper, who was obsessed with the Green Arrow (obviously we know Roy is Thea's boyfriend in the show). Speedy was Green Arrows side kick for some time and then morphed in to the Red Arrow (Notice how he carries around one of Oliver's arrows that's painted red). Laurel Lance in the comic book was the Black Canary, another one of Oliver's "side kicks". I use that term loosely here, as she was mostly a hero herself but worked with Oliver closely. Obviously they took another route in the show promoting this random assassin girl to Black Canary and Laurel to just a normal love interest (which is really weird since you clearly was kicking peoples asses in the early episodes. This makes me wonder if she'll eventually take up that mantle).
Now on to the League/Amazo. Amazo is basically an android made by a scientist that worked for S.T.A.R. Labs. Amazo is a heavy hitter in the DC universe, not a chump like Merlyn or Brutale that Oliver can take on his own. He's a regular Villain of the JLA (Justice League of America) and often times required Superman, Wonder Woman, Batman, Flash, Etc. to step in and take care of him. It's really big that they'd mention him in the show because if he's going to be fighting Amazo sometime in the future, they almost absolutely need to add in a cameo from a "Super hero" one that has extra ordinary powers that are greater than just shooting a bow. Unless they really change him and turn him in to a giant pussy, which leads to the next answer ...
The rest of the DC universe must exist in the show. Starling city (Star City) was Green Arrows regular stomping grounds in the comics, so it would make sense if Metropolis, Gotham, Etc. all did as well. With the now Black Canary being exposed as a target of interest for Ras Al Ghul (aka one of Batmans arch enemies) that sets up a whole new situation where we could see a cameo and almost affirms the existence of, well, basically everyone in the universe existing within this one. Ra's Al Ghul is another target that Black Canary or Green Arrow probably are out classed by. He's old (couple hundred years), really smart, really strong/durable, and can't die due to the Lazarus Pit. Also the girl is a "good guy" but she would for sure show up Oliver in any fight, which I can't really see the creators of the show doing.
Now the Amazo sentiment might be wrong, it may just be a nod to the comic books, since they do that QUITE often in this show. For instance the first "Deathstroke" that they killed in the camp on the island was Wintergreen a villain in the universe that had basically nothing to do with Deathstroke, they just gave him the name because he was there. The guy getting off the helicopter that was killed instantly, he was Brutale in the comic books, wore a full body suit had big metal appendages like doc oc and shot daggers. He was nearly killed INSTANTLY. Thea having the nickname Speedy. The list goes on for quite a while.
I grew up reading comics, mostly Marvel and my knowledge of DC is pretty limited so I'll try to answer any questions if you guys have more.