A creature can do what it wants while affected by the spell maze, including trying to escape

A creature doesn't have to, but it may try to escape the maze effect:

Each round on its turn, it may attempt a DC 20 Intelligence check to escape the labyrinth as a full-round action.

That is, the option to make an escape attempt is available in addition to whatever the creature could normally do. This is further supported later in the spell's description:

Spells and abilities that move a creature within a plane, such as teleport and dimension door, do not help a creature escape a maze spell, although a plane shift spell allows it to exit to whatever plane is designated in that spell.

This strongly suggests that, instead of trying to escape by making an Intelligence check, a creature can do other things like, for example, cast spells (including the spell plane shift to escape). Note that, while affected by the spell maze, the creature is in an extradimensional space, and this may limit the creature's options.

Previous versions of the spell maze were more... confining

Some older versions of the spell maze from Pathfinder's antecedent Dungeons and Dragons did, in fact, restrict a creature affected by the spell maze from doing anything but experiencing the labyrinth or trying to escape. For example:

• The Player's Handbook (1978) for Advanced Dungeons and Dragons has this as part of the description of the spell maze:

The recipient will wander in the shifting labyrinth of force planes for a period of time which is totally dependent upon its intelligence. (90)

Emphasis mine. (It should be known that I have always interpreted this as the affected creature being restricted to just wandering, but another DM may interpret this differently.)

• The Player's Handbook (1995) for Advanced Dungeons and Dragons, 2nd Edition subtly changed the AD&D spell's description:

The subject vanishes into the shifting labyrinth of force planes for a period of time which is dependent upon its Intelligence. (241)

Emphasis mine. Yet, in the Dragon #170 Sage Advice column, the Sage addresses this issue head-on:

The spirit of the spell description suggests that the nature of the labyrinth created by the maze spell prompts the victim to escape as soon as possible, and that no actions other than escape are possible while a victim is within. The victim can try a spell to get out, but he cannot do anything that does not contribute directly to escape.

It wasn't until the maze spell appeared in the Player's Handbook (2000) for Dungeons and Dragons, Third Edition that a creature could—absolutely and without risking violating the spell's letter or spirit—do something other than try to escape the effect of the spell maze, that version of the spell having much the same text as the Pathfinder spell does now.