Adding dynamic ui in data table output

You are trying to do something quite complicated, it requires js callbacks in DT and use of bind and unbind etc.
Here is an example

library(shiny)
library(DT)
shinyApp(
  ui <- fluidPage(
    title = 'Slider Inputsa table',
    DT::dataTableOutput('foo'),
    verbatimTextOutput('sel')
  ),
  server <- function(input, output, session) {
    m <- matrix(
      1:12, nrow = 12, ncol = 1, byrow = TRUE,
      dimnames = list(month.abb, "initial_slider_values")
    )
    m2 <- m
    for (i in seq_len(nrow(m))) {

      m2[i, ] <-selectInput(inputId = month.abb[i],
                          label = month.abb[i],
                          choices = c(m[i, ],m[i, ]-1),
                          selected = m[i,]) %>% as.character
      }
    m2
    output$foo = DT::renderDataTable(
      m2, escape = FALSE, selection = 'none', server = FALSE,
      options = list(dom = 't', paging = FALSE, ordering = FALSE),
      callback = JS("table.rows().every(function(i, tab, row) {
          var $this = $(this.node());
          $this.attr('id', this.data()[0]);
          $this.addClass('shiny-input-slider-input');
        });
        Shiny.unbindAll(table.table().node());
        Shiny.bindAll(table.table().node());")
    )
    output$sel <- renderPrint({
      str(sapply(month.abb, function(i) input[[i]]))
    })
  }
)

I adapted this from
Radio buttons in a table (shinyapps.io)