We can add mygroup as another column in the rolling join:
df[, date := as.Date(date)]
df[
  df[, .(date = seq(first(date), last(date), by="day")), by=mygroup], 
  on=.(mygroup, date), 
  roll=TRUE]
          date       value mygroup
 1: 2017-01-01 -0.56047565       A
 2: 2017-01-02 -0.56047565       A
 3: 2017-01-03 -0.56047565       A
 4: 2017-01-04 -0.56047565       A
 5: 2017-01-05 -0.23017749       A
 6: 2017-01-06 -0.23017749       A
 7: 2017-01-07 -0.23017749       A
 8: 2017-01-08  1.55870831       A
 9: 2017-01-01  0.07050839       B
10: 2017-01-02  0.07050839       B
11: 2017-01-03  0.07050839       B
12: 2017-01-04  0.07050839       B
13: 2017-01-05  0.12928774       B
14: 2017-01-06  0.12928774       B
15: 2017-01-07  0.12928774       B
16: 2017-01-08  1.71506499       B
The "rolling" always happens on the final column in on=.
If the table had more columns and we only wanted to fill back some of them...
# extend example
set.seed(1)
df[, y := rpois(.N, 1)]
# build new table
newDT = df[, .(date = seq(first(date), last(date), by="day")), by=mygroup]
roll_cols = "value"
newDT[, (roll_cols) := 
  df[newDT, on=.(mygroup, date), roll=TRUE, mget(paste0("x.", roll_cols))]]
noroll_cols = "y"
newDT[df, on=.(mygroup, date), (noroll_cols) := mget(paste0("i.", noroll_cols)) ]
    mygroup       date       value  y
 1:       A 2017-01-01 -0.56047565  0
 2:       A 2017-01-02 -0.56047565 NA
 3:       A 2017-01-03 -0.56047565 NA
 4:       A 2017-01-04 -0.56047565 NA
 5:       A 2017-01-05 -0.23017749  1
 6:       A 2017-01-06 -0.23017749 NA
 7:       A 2017-01-07 -0.23017749 NA
 8:       A 2017-01-08  1.55870831  1
 9:       B 2017-01-01  0.07050839  2
10:       B 2017-01-02  0.07050839 NA
11:       B 2017-01-03  0.07050839 NA
12:       B 2017-01-04  0.07050839 NA
13:       B 2017-01-05  0.12928774  0
14:       B 2017-01-06  0.12928774 NA
15:       B 2017-01-07  0.12928774 NA
16:       B 2017-01-08  1.71506499  2