Ytdyklly

The tall figure was overwhelmingly tall. It stood in the corner of the
room. The skinny figure right beside him sat on a chair. It wasn't
moving at all. The tall figure moved to the opposite side of the room
and started palpating the wall as if it was looking for something. The
skinny figure then started crawling and palpating the floor as if it
were looking something. The tall figure then started laughing loudly
and clapping his hands as if it were overjoyed. The skinny figure
hearing this started doing the same.

How do I minimize the amount of repetition? Is there a way of doing this without changing drastically the sentences? What would you suggest? As you can see, I used "it" immediately after using the adjective-noun pairs but, when I switch person, I have no choice but to use the appropriate adjective-noun pair.

You have a few choices here:

1. You can group each person's actions together more (I've also edited a couple errors).

The tall figure was overwhelmingly tall. It stood in the corner of the
room then moved to the opposite side of the room and started palpating
the wall, as if it was looking for something. Then it started
laughing loudly and clapping its hands as if it were overjoyed.

The skinny figure sat right beside the tall one on a chair. It wasn't
moving at all. It then started crawling and palpating the floor as if
it were looking for something. When the tall figure was laughing and
clapping the skinny figure started doing the same.

2. You can name the characters. If you don't want to use real names, try the characteristics.

Tall was overwhelmingly tall. It stood in the corner of the room.
Skinny right beside it sat on a chair. It wasn't moving at all. Tall
moved to the opposite side of the room and started palpating the wall
as if it was looking for something. Skinny then started crawling and
palpating the floor as if it were looking for something. Tall then
started laughing loudly and clapping its hands as if it were
overjoyed. Skinny hearing this started doing the same.

3. You can make them different genders. Instead of making them both "it" (with some accidental? "he" in there), make one "he" and one "she."

The tall figure was overwhelmingly tall. He stood in the corner of the
room. The skinny figure right beside him sat on a chair. She wasn't
moving at all. He moved to the opposite side of the room and started
palpating the wall as if he was looking for something. She then
started crawling and palpating the floor as if she were looking for
something. He then started laughing loudly and clapping his hands as
if he were overjoyed. Hearing this, she started doing the same.

You can look for other ways to identify the characters. For example:

The tall figure stood in the corner, towering over the unmoving skinny figure in the chair beside it. It moved away from the seated figure to the opposite side of the room and began palpating the wall as if looking for something. The other figure crawled from the chair and began palpating the floor. (etc)

In this example, "towering over" avoids repeating that the tall figure was very tall, "unmoving" avoids saying that the skinny figure wasn't moving, and once you know the identity of one you can refer to the "other". The riskiest thing in my version, clarity-wise, is who moved away, because the "it" could be ambiguous. That's why I said it moved away from the seated figure; that tells you who's acting by process of elimination.

I've stuck with your sparse description here, but if you had described the figures more, you could make use of that too -- referring to someone's lanky legs, blond locks, frayed cloak, or whatever.

You can identify characters in ways other than the noun phrases you used to introduce them.