If you progress in the game to the point where you're meant to input the word 'game' into some spaces, the narrator will say "Are you going to try every word in the dictionary?" My answer: Yes! Yes I am!
We have these letters:

E R A T E O M G

The game intends for you to write "Goat", "Game", and "Tree", but what else can we make with these letters? Let's see!

A
-Ate (no clue how I missed this one)
-Atom

E
-Ear
-Eat
-Egg
-Emote

G
-Game(r)
-Gate
-Gear
-Germ
-Goat
-Gore
-Got
-Gum

M
-Mage
-Mart
-Mat
-Mate
-Meat
-Meet
-Mere
-Met
-Meta
-Meteor (thanks, Bonitar!)
-Moat
-More

O
-Ogre
-Ore

R
-Rage
-Rat
-Rate
-Remote
-Roam
-Rome
-Rot

T
-Tame
-Tar
-Tea
-Team
-Tear
-Term
-Toe
-Toga
-Tom
-Tome
-Tore
-Tram
-Tree



Feel free to let me know if I've missed anything!

The rat is named Nora.
Notice the letters in "theRe is NO gAme"?
It has Nora in it!