Basically, the SPARQL you are doing is too expensive. Right above the dashboard header there is a collection of Query service links :

all entities | count | all groupings | without grouping property | below threshold (200)

These are a subset of the SPARQL queries that integraality will do. If the all entities or all_groupings queries do not pass in the Query Service, then integraality will likely fail too. Your best shot is to either settle for a less advanced selection, or use some fancier faster SPARQL. I tried a bit with the following (assuming I understood what you intended correctly), it might work:

SELECT ?entity ?entityLabel ?entityDescription ?st ?sl ?ids WHERE {
  ?entity (wdt:P31/(wdt:P279*)) wd:Q163740.
  VALUES ?exclude {
      wd:Q7278
      wd:Q4438121
      wd:Q1030034
  }
  MINUS {
    ?entity (wdt:P31/(wdt:P279*)) ?exclude.
  }
}

(I thought I handled such time outs better, to give the user some clue − looks like I’m still missing some error handling)