Bsrgvty

Loop steps from 1 through 9. Each step puts current index digit of the loop into a box and extracts the digit's width. The width is then appended as dimension value to a sequence. Although the sequence contains 9 values at the end, oddly all of them are dimension (width) of digit 9. All values of the sequence are overwritten to new dimension at each step. Maybe you can figure out the core of the problem.

documentclass[varwidth=100mm]standalone
usepackageexpl3
usepackagefontspec
setmainfontImpact
begindocument
ExplSyntaxOn

seq_new:NmySeq
box_new:NmyBox
int_step_inline:nn9
 hbox_set:NnmyBox#1
 % display dimension before adding it to sequence
 #1=dim_eval:nbox_wd:NmyBox\ % output
 % add dimension to sequence
 seq_put_right:NnmySeq
 dim_eval:nbox_wd:NmyBox
 % display current contents of the sequence
 seq_use:NnmySeq_\\
 
% display all dimensions (contains only duplicates of last dimension)
seq_use:NnmySeq,~

ExplSyntaxOff
enddocument

You need to expand the value: use

seq_put_right:Nx

instead.

What's the problem? If you do

hbox_set:Nn l_tmpa_box A 
seq_put_right:Nn l_tmpa_seq dim_eval:n box_wd:N l_tmpa_box 
hbox_set:Nn l_tmpa_box AA 
seq_put_right:Nn l_tmpa_seq dim_eval:n box_wd:N l_tmpa_box 

this results in the sequence to contain the following items (without the outer braces, as it would be displayed by seq_show:N l_tmpa_seq)

 dim_eval:n box_wd:N l_tmpa_box 
 dim_eval:n box_wd:N l_tmpa_box 

When the sequence is used, the width of the current contents of l_tmpa_box is employed: the value it had at the moment of assignment has never been mentioned.

With seq_put_right:Nx you instead get the value frozen at the moment of the assignment.

Would it be “better” to use

exp_args:NNx seq_put_right:Nn l_tmpa_tl ...

No. Using (or defining, in case of need) a variant is better style.

When you do:

seq_put_right:Nn mySeq dim_eval:n box_wd:N myBox 

what you are appending to your sequence is the token list dim_eval:nbox_wd:NmyBox (the tokens are dim_eval:n, with catcode 1, box_wd:N, myBox and with catcode 2). The final dim_eval:n is evaluated too late, once the loop has been fully executed and you do seq_use:Nn mySeq ,~. At this point, myBox contains the digit 9, hence what you saw. As egreg said (faster than me), replace seq_put_right:Nn with seq_put_right:Nx to evaluate dim_eval:n inside the loop, when myBox still contains the relevant digit.

You have to realize that your sequence variable mySeq does not contain any length at all: it contains n times the same token list, which I explicitated above, with n=0 at first, then n=1, ..., and finally n=9. In other words, it contains n times the same “formula,” stored in the form of a token list. This formula is comparable to a function of one variable, the box variable myBox. Whenever you use seq_use:Nn mySeq ..., you put n copies of the same formula in the input stream (where n is the current length of mySeq), and when TeX expands one of the dim_eval:n tokens and processes all tokens resulting from this expansion, this yields a length (precisely: a 〈dimen〉) according to the formula and the contents of myBox at that point.

At the end of your example, your code therefore computes n=9 times the same formula with the same value of myBox, an hbox containing the figure 9. In very explicit terms, your final seq_use:Nn call is equivalent to this:

dim_eval:n box_wd:N myBox ,~
dim_eval:n box_wd:N myBox ,~
dim_eval:n box_wd:N myBox ,~
dim_eval:n box_wd:N myBox ,~
dim_eval:n box_wd:N myBox ,~
dim_eval:n box_wd:N myBox ,~
dim_eval:n box_wd:N myBox ,~
dim_eval:n box_wd:N myBox ,~
dim_eval:n box_wd:N myBox 

Calculating 9 times f(x) with the same function f and the same value of x gives 9 times the same result, hence the output you obtained.

For the seq_use:Nn calls inside the loop, this is exactly the same, except that n is replaced by a number between 1 and 8, inclusive.

Note: as people already told you, your variables don't respect the LaTeX3 coding guidelines. Read expl3.pdf and l3styleguide.pdf from here (the beginning of interface3.pdf is also pretty useful to read at first, but I suppose you've already seen it).