The dialogue is very childlike and excludes a lot of proper grammar, so it looks like the translation on the link you posted was pretty good.

If you want a second opinion, this is how I'd write it:
H-h-h-hey, hey, a moment please?
If you're busy, I'm sorry
Just a little, hey, just a little would be nice (as in, "just a little bit of your time")
We can hang out and chat
What are we gonna do? What should we do?
Well... how bout we play a game?
We should play Shiritori (a Japanese word game)
Shirato"ri"... "ri"n.**
Sorry, let's not continue...
**
(In Shiratori, players take turns naming off nouns that end with the final kana of the previous word. However, the player who names a word that ends in "n" loses, because no Japanese words start with "n", so the game is over. So what happens in the song is that she tries to start the game by playing off the word "shiratoRI", except she picks the word "RIn", ending in "n", so she loses.
)
Are you hungry? Do you want something to eat?
Well, for me... water will be fine
You looked away from your monitor
And immediately, I frantically simulated
But despite this, you idiot, with you staring at me
I feel thirsty, and can't speak anymore
Whew... what should I do?
You know, the truth is...
No, I'm too afraid after all
I want to tell you how I feel
Why are these feelings so painful?
H-h-h-hey, hey, a moment please?
If you're busy, I'm sorry
Just a little, hey, just a little would be nice
We can hang out and chat
What are we gonna do? What should we do?
Well... we should play that ja-ja-janken (Japanese rock-paper-scissors game)
Jankenpon! Looks like a tie... (Players say "jan-ken-pon" during gameplay)
Sorry, this is boring, huh?
Are you hungry? Do you want something to eat?
Well, for me... water will be fine
But you know, by the way, suddenly...
If you think this is silly, I'm sorry
You might be surprised
But I want you to listen, well...
Whew... what should I do?
You know, the truth is...
No, I'm too afraid after all
I want to tell you how I feel
Why are these feelings so painful?
(From here on, you probably picked up on how she stutters through what she's trying to say, which is adorable, but impossible to match up in English perfectly since Japanese grammar is so different than ours.
)
You know, the truth is,
I-I, I-I, well, well...
You know, you--, ah...
I, I'm sorry, wait... I-I...
I-I, well, you know...
You--, (I) li--
You know, the truth is that, I... I--
I, well, well, you know...
You--, ah...
I, I'm sorry, wait, well, you know
Eh... I...
It's you that I--!
You know, I, it's you...
You know, I, it's you...
It's you that I...
L-l-li-li, li-li, l...l...
L-l-l-l, l--, l--, l--, l--
Liii, haa... I'm sorry, forget it
...Wait!
L-l, l-l, l-l-l-l...
L-l-l-l, l-- l-- l-- l--
L-- l--, l-l, l-l, l-- l--
I LIKE YOU, I LOVE YOU!!!!
---------------------------------------
Kanji from (
this page):
ねねねねえ、ね、ちょっといい?
忙しいなら、ごめん
少しだけ、ね 少しでいい
お喋りに付き合って
どうしようか? 何しようか
えっと
ゲームでもする?
しりとりしよ
しりと「り」
「り」ン。
ごめんね、続かないね
おなか空かない? 何か食べたい?
ええと、あたし
水でいいや
君モニタから 目を離した
隙に 必死に シミュレート
それなのにバカ 見つめられたら
喉が乾いて 声でない
ぷはぁ
どうしよう
あのね、実はね
ダメだ、やっぱり怖いの
気持ち 伝えた いよ あなたに
この 気持ち どうし て 苦しいの
ねねねねえ、ね、ちょっといい?
忙しいなら、ごめん
少しだけ、ね 少しでいい
お喋りに付き合って
どうしようか? 何しようか
えっと
それじゃじゃジャンケンしよ
じゃんけんポン あいこでしょ
ごめんね、つまらないね
おなか空かない? 何か食べたい?
ええと、あたし
水でいいや
あのね、ところで、唐突だけど
おかしいって思ったらごめん
びっくりする かもしれないの
でもね、聞いて欲しい、ええと
ぷはぁ
どうしよう
あのね、実はね
ダメだ、やっぱり怖いの
気持ち 伝えた いよ あなたに
この 気持ち どうし て 苦しいの
あのね、実は、
あたあたし、あた、あたし、あの、あの
あのね、あなたが、ああ、
あたし、ごめん、待って
あたあたし
あた、あたし、あの、あのね、
あなたが、す
あのね、実はのその、あたし、あた
あたし、あの、あの、あのね、
あなたが、ああ
あたし、ごめん、待って、あのあのね
ええと、あたし
あなたのことが
!
あのね あたし あなた のこと
あのね あたし あなた のこと
あたしは あなたが
す、す、すす、すす、す
す
すすすす、す、す、す、す、
すう、はあ
ごめん、忘れて
待って!
す、す、すす、すすすす
すすすす、す
す
す
す
す、す、すす、すす、す
す
すき、だあいすき!!!!
----------------------------------
These are the changes I would make to the roomaji. I think the words were fine, just broken up strangely.
ne ne ne nee, ne, chotto ii?
isogashii nara, gomen
sukoshi dake, ne sukoshi de ii
oshaberi ni tsukiatte
dou shiyou ka? nani shiyou ka?
etto... GAME demo suru?
shiritori shiyo
shirito"ri"... "ri"n.
gomen ne, tsudukanai ne...
onaka sukanai? nani ka tabetai?
eeto, atashi... mizu de ii ya
kimi MONITOR kara me o hanashita
suki ni hisshi ni SIMULATE
sorenanoni baka mitsumeraretara
nodo ga kawaite koe de nai
puhaa... dou shiyou
ano ne, jitsu wa ne...
dame da, yappari kowai no
kimochi tsutaetai yo anata ni
kono kimochi dou shite kurushii no
ne ne ne nee, ne, chotto ii?
isogashii nara, gomen
sukoshi dake, ne sukoshi de ii
oshaberi ni tsukiatte
dou shiyou ka? nani shiyou ka?
etto... sore ja ja janken shiyo
jankenpon aiko desho
gomen ne, tsumaranai ne
onaka sukanai? nani ka tabetai?
eeto, atashi... mizu de ii ya
ano ne, tokoro de, toutotsu dakedo
okashii tte omottara gomen
bikkuri suru ka mo shirenai no
demo ne, kiite hoshii, eeto...
puhaa... dou shiyou
ano ne, jitsu wa ne...
dame da, yappari kowai no
kimochi tsutaetai yo anata ni
kono kimochi dou shite kurushii no
ano ne, jitsu wa,
ata atashi, ata, atashi, ano, ano
ano ne, anata ga, aa,
atashi, gomen, matte ata atashi
ata, atashi, ano, ano ne,
anata ga, su...
ano ne, jitsu wa no sono, atashi, ata
atashi, ano, ano, ano ne,
anata ga, aa...
atashi, gomen, matte, ano ano ne
eeto, atashi...
anata no koto ga...!
ano ne atashi anata no koto
ano ne atashi anata no koto
atashi wa anata ga...
su, su, susu, susu, su... su
susu susu, su, su, su, su,
suu, haa... gomen, wasurete
...matte!
su, su, susu, susu susu
susu susu, su... su... su... su
su, su, susu, susu, su... su
suki, daisuki!!!!