yeah basically
but the blocks on the side only need to check those sides which actually contain spaces for blocks

Yup pretty much.
While you need at most two checks per tile, you need to check 15 of them. Not the last one.

HI AGAIN GUYS!
(sorry my happiness is exploding)
So the game's all done, thanks to pikachu and the walrus for the help. Here's a gif of how it works :

and here's the code :




.A2048
[FF818181818181FF]->Pic0
[FF818199998181FF]
[FF8189B99D9181FF]
[FF81FF8181FF81FF]
[FF81BDA5A5BD81FF]
[FFA5FFA5A5FFA5FF]
[FF9999FFFF9999FF]
[FFC3A59999A5C3FF]
[FFC3BDBDBDBDC3FF]
[FFFFC3DBDBC3FFFF]
[FFFFFFE7E7FFFFFF]
[FFABD5ABD5ABD5FF]
[FFFFFFFFFFFFFFFF]
DeltaList(40,16)->Pic1
[FFFFF0FF00818190818081819F8180F999999980F999999980819981818081998181809F99F999809F99F9998081818981808181898180FFFF8FFF807FFF87FF80000000000000000000000000000000]


DiagnosticOff
ExprOn
Full
Fix 5
Fill(L1,16,0)
0->I->J->K
1->{L1+16}


UnArchive "|vA"
!If GetCalc("|vA"
GetCalc("|vA",20)->Q
R()
Else
GetCalc("|vA")->Q
End
LOAD()
GUI()


Repeat getKey(15)
If getKey
If getKey(1)
DOWN()
End
If getKey(2)
LEFT()
End
If getKey(3)
RIGHT()
End
If getKey(4)
UP()
End
If getKey(55)
R()
End
If getKey(54)
H()
End
GO()
If S>{Q+18}^^r
S->{Q+18}^^r
End
If S!=W
TEXT()
S->W
End
End
D()
End
SAVE()
ClrDraw^^r^^r
Return




Lbl DOWN
0->theta
For(J,0,3)
3->N
For(K,1,3)
3-K->I+1->X
If {4*I+J+L1}->V!=0
Repeat {4*X+J+L1}->T=V or (T!=V and (T!=0)) or (X=N)
X++
End
{4*X+J+L1}->T
If T!=V and (T!=0)
X--
End
If X!=I
If {4*X+J+L1}=0
V->{4*X+J+L1}
Else
V+1->{4*X+J+L1}
X-1->N
e^(V+1)+S->S
End
0->{4*I+J+L1}
theta++
End
End
End
End
If theta
N()
End
Return


Lbl LEFT
0->theta
For(J,0,3)
0->N
For(I,1,3)
If {4*J+I+L1}->V!=0
I-1->X
Repeat {4*J+X+L1}->T=V or (T!=V and (T!=0)) or (X=N)
X--
End
{4*J+X+L1}->T
If T!=V and (T!=0)
X++
End
If X!=I
If {4*J+X+L1}=0
V->{4*J+X+L1}
Else
V+1->{4*J+X+L1}
X+1->N
e^(V+1)+S->S
End
0->{4*J+I+L1}
theta++
End
End
End
End
If theta
N()
End
Return


Lbl RIGHT
0->theta
For(J,0,3)
3->N
For(K,1,3)
3-K->I+1->X
If {4*J+I+L1}->V!=0
Repeat {4*J+X+L1}->T=V or (T!=V and (T!=0)) or (X=N)
X++
End
If (T!=V and (T!=0))
X--
End
If X!=I
If {4*J+X+L1}=0
V->{4*J+X+L1}
Else
X-1->N
V+1->{4*J+X+L1}
e^(V+1)+S->S
End
0->{4*J+I+L1}
theta++
End
End
End
End
If theta
N()
End
Return


Lbl UP
0->theta
For(J,0,3)
0->N
For(I,1,3)
I-1->X
If {4*I+J+L1}->V!=0
Repeat {4*X+J+L1}->T=V or (T!=V and (T!=0)) or (X=N)
X--
End
{4*X+J+L1}->T
If T!=V and (T!=0)
X++
End
If X!=I
If {4*X+J+L1}=0
V->{4*X+J+L1}
Else
X+1->N
V+1->{4*X+J+L1}
e^(V+1)+S->S
End
0->{4*I+J+L1}
theta++
End
End
End
End
If theta
N()
End
Return


Lbl SAVE
conj(L1,Q,16)
S->{Q+16}^^r
Return


Lbl LOAD
conj(Q,L1,16)
{Q+16}^^r->S
Return


Lbl N
16->L
Repeat {L1+L}=0
rand^16->L
End
rand^6/5+1->{L1+L}
Return


Lbl R
0->S->W
Fill(L1,16,0
N()
N()
Return


Lbl GO
0->H
For(I,0,15)
If {I+L1}=0 or (I<12 and ({I+4+L1}={I+L1})) or (I^4!=3 and ({I+1+L1}={I+L1}))
1->H
End
End
!If H
Pause 300
ClrDraw^^r^^r
If S={Q+18}^^r
RECT(20,17,56,30,~1)
Text(30,20,"Game Over!")
Text(28,28,"Score:",S>Dec)
Text(23,36,"New Highscore!")
Else
RECT(24,21,47,21,~1)
Text(29,24,"Game Over!"
Text(27,32,"Score:",S>Dec)
End
DispGraph
Repeat getKey
End
R()
GUI()
End
Return


Lbl H
ClrDraw^^r^^r
For(I,0,11)
Pt-On(I/6*48+20,I^6*9+5,I+1*8+Pic0)
If I<6
Text(29,I*9+6,e^(I+1)>Dec)
End
End
Text(56,6,"128")
Text(56,15,"256")
Text(56,24,"512")
Text(52,33,"1024")
Text(52,42,"2048")
Text(52,51,"4096")
Text(58,58,"by Toctave"
DispGraph
Repeat getKey
End
GUI()
Return


Lbl RECT
HLine({r2},{r1}-{r5},{r1}+{r3}+{r5}
HLine({r2}+{r4},{r1}-{r5},{r1}+{r3}+{r5}
VLine({r1},{r2}-{r5},{r2}+{r4}+{r5}
VLine({r1}+{r3},{r2}-{r5},{r2}+{r4}+{r5}
Return


Lbl GUI
ClrDraw^^r^^r
Tangent(32,3,Pic1
For(I,0,15)
Pt-On(I^4*9+31,I/4*9+21,Pic0)^^r
End
RECT(29,19,38,38,1
RECT(70,21,24,14,~1
RECT(70,38,24,14,~1
TEXT()
Return


Lbl D
For(I,0,15)
If {L1+I}
Pt-On(I^4*9+31,I/4*9+21,{L1+I}*8+Pic0)
End
End


DispGraph^^r
Wref(31,21,35,35)
Return


Lbl TEXT
Text(72,22,"Score:"
Text(73,28,S>Dec
Text(75,39,"Best:"
Text(73,45,{Q+18}^^r>Dec
VLine(94,45,50)
VLine(94,28,33)
Return

Fix 4What I changed :
-The GUI doesn't update every loop anymore, it now has its own subroutine GUI()
-Same for text, it only updates when needed with TEXT()
-Game Over is now supported, whenever you're stuck, the game stops and displays a window with your score and highscore if you beat it, then waits for any key and resets, it's subroutine GO()
-Every display bug is fixed, the text does not flash like an epileptic mouse anymore

could you upload a compiled version?
i'm too lazy to download tokenIDE again

Oooh that looks quite nice, and I like the different tile style replacing numbers with drawings.

Would animated blocks be feasible? I think if you did that you should make the moving blocks monochrome while they are still moving, so the grayscale won't look weird.

You can do that while you compute the tile movement.