Its sort of like Risk... but comparing it to Risk isn't fair. It makes Risk feel like a game for toddlers.
A&A is for reals. There's like a dozen different units, each with different strengths and weaknesses... (infantry attack weaker and move slower than tanks, but cost less and therefore you can get more of them to soak up hits).
And yeah it's based on WW2. There's 5 powers... the Allies (USSR, UK, USA) vs the Axis (Germany, Japan). Each power makes their own income based on owned territory minus any economic attacks. Spend money on units or occasionally developing tech to make your units better.
AARe rules add a bunch of other awesome stuff, like having each power pick from a list of national advantages (Russian Railway lets USSR bring their infantry to the front line faster, German 88s let you mow down defending units without giving them the chance to fire back, Japanese Kamikazes let you sacrifice fighters to blow up approaching naval units, etc. Each power has 6 advantages to choose from).
If by rush you mean "hurry up and finish your turn"... no. It's turn based and fairly slow moving. One round (all 5 powers getting a turn) can easily take over an hour.
If you mean rush as in "attack aggressively before they have a chance to build up a defense"... it depends. Different strategies use different tactics.
Although the Allies have a money advantage, so generally speaking the longer the game lasts the better things look for the Allies. That's not always the case, though, as there are strategies to neuter the UK economically so that the money is fairly even.
Allies strategy: Kill Germany first
Probably the most typical Allied strategy. Put minimal focus on Japan and just hit Germany as hard as you can as fast as you can. If Germany is fighting 3 fronts they will not be able to advance on Russia... so all you have to do is reach Germany before Japan reaches Russia.
US Strategy: Go through Africa!
With the "mechanized infantry" advantage, infantry+tanks can blitz through and reclaim Africa pretty quick. They can eventually get to India and keep Japan at bay while Russia and UK hold off Germany. Once you get to that point, the Axis simply can't keep up with Allied money (especially not without Africa) and it's just a matter of wearing them down.
You can do a one-turn transport from Eastern Canada to Algeria which means with 4 transports you can start shipping 8 land units a turn into Africa pretty early.
Axis Strategy: Hardcore wolf packs
Have Japan use its Tech Advantage NA to get Super Subs first turn. Then buy Super Subs with Germany on turn 2 for a cheaper rate. That + Wolf Packs advantage means you have subs that do massive economic damage, attack at 4, and only cost $7 to produce.
Keep your subs back so UK can't reach them, and pounce on any boats the UK tries to build. Buy 2+ subs every turn. If you secure the Atlantic, you can even start doing economic damage to the US (although if you can get that far, you've pretty much won the game unless Japan really blows it)
If USA doesn't go towards Germany, this strategy DESTROYS the UK and prevents them from transporting any land units / making any money. (but an experienced Allied player will recognize it)
Japan strategy: Ignore the US
It's tempting to attack Hawaii first turn to blow up that Carrier... but unless the US decides to attack Japan (which is very hard to do effectively), the carrier is meaningless. So let them have it!
First turn, build 2 factories in mainland Asia (Kwangtung and Indochina, usually... but Kwangtung and Manchuria is a safer/slower bet) and wipe out whatever remains of the UK navy in the Pacific. Get your navy back on the Pacific coast of Asia and start building 6+ land units every turn by turn 2. Bust in on Russia ASAP.
If you can poise to take India on turn 2, even better. Just don't forget that China is more important.
If the US decides to head west, you'll have to adjust your strategy. Your attack on Russia will be slowed, but you can get away with buying only infantry and letting your airforce do the work. Use remaining money to buy boats to stay ahead of the US's navy. If the US doesn't take Reinforced Carriers, consider getting Kamikazes or Kaitens to pick them off. The US is not nearly as intimidating without carriers.
German strategy: Hold the coast
Turn 1: build a carrier and a transport to put in the German SZ to prevent UK from wiping it out. Transport guys to Norway to reinforce it. Take Atlantic Wall as your advantage.
Turn 2: Take German 88's as your other advantage. Build a factory on Norway (assuming you held it... if you didn't, blow the UK navy out of the water and take it back, then build the factory on turn 3).
Atlantic wall + 88s makes it very hard/dangerous for UK to get any land units in Europe. The occasional sub purchase in Norway will slow them down even more (and possibly give you a chance to pick off boats with your 'Coastal Defense').
Downside: you will not be able to advance on Russia.
Largely a defensive strategy. If Japan can't move in fast, it won't work.
This is really making me want to play this now... hahaha
German Strategy: fast fast fast
Germany starts with like 10 tanks or something crazy like that. So turn 1: get panzerblitz! Buy all infantry first turn, then buy ~2 tanks + as much infantry you can afford after that. Use panzerblitz right and you will never lose tanks. Couple that with the Luftwaffe advantage and you've got a powerful, undying attack force. The hard part is keeping enough infantry on the front lines.
Alternatively, Africa Korps first turn and Panzerblitz second turn works well. Also if you want to go hardcore you can buy all tanks 1st turn instead of all infantry. That's sort of going balls to the wall, though, and if it doesn't work you'll have to fall back and it'll take time to regroup.
Hardest part about this strategy is finding out a way to hold Western Europe. Especially if the US is going east. Maybe Atlantic Wall + Panzerblitz?
The goal is get + hold Caucasus ASAP. Once you do that, Russia is all but neutralized and you can work on fighting back against UK/US. Of course getting Caucasus is easier said than done.