Its not just the expanding. In non-money maps u also cant afford to lose units. If ur units are attacked u have to pull back or micro, u cant waste them. 3 zealots + 2 probes can make a lot of trouble for a zerg player in early game, the player with the best unit controll will win that battle.
Expanding is needed because u will run out of money. To constantly produce units out of many gateways u need money, and lots of it. In late game each player will have 2-3 bases and 2-3 minor expansions. Zerg players will have 4-5 expansions after 10 minutes to provide money for macro. Its all about the money. The goal of the game is not to destroy the enemy's main base, it is to keep him down economically by constantly striking workers and expansions.
The terrain is important in maps like LT. If u drop units on the cliffs above expansions it is harder to stop the drop because of the isolation. Units on low ground only have a 70% chance of hitting the target on top of the cliff, the same is for units hideing behind a tree. Also, units on low ground cant see units on high ground unless they are shooting at them, so u can create a suprise attack by using cliffs.
Cliff ramps, bridges and other choke points can make a really big difference. U cant send 40 hydras to attack through the ramp to his main base, they will be dead right away because they will be split up when only 4-5 can go up at once and the first ones will stop to attack. 4 siege tanks on a cliff can probarbly kill 50 marines without any problems. U have to think more strategically and drop in his peon line to kill his echonomy, or attack from many sides.
Ramps can be used to stop zergling rushes by placing 2 zealots to block the entrance. This way, only 2 zerglings will be able to attack the zealots at one time, so the zerg will have to pull back or lose his zerglings.
Non-money maps require a lot more strategy than money maps, the only thing money maps are good for is practicing micro.