Let's see if this helps.
According to "Irvines and Their Kin" William de Irwyn 1st Laird of Drum was married to the daughter of the Earl Marischal.
"William De Irwyn, or Sir William Irvine, as he is styled in "Nisbet's Heraldry," married Mariota, the daughter of Sir Robert Keith, Earl Marischal of Scotland, who led the horse at Bannockburn, and was killed at the battle of Dublin {sic} in 1332".
"The Irvines of Drum and Collateral Branches", in general, agrees with this.
https://www.geni.com/photo/view?album_type=photos_of_me&id=6000...
it says "daughter OR grand-daughter" but ages of parties involved suggest "daughter" is the more reasonable.
So: Yes he had daughters.
However, someone has changed the date and location of his death. He died : 11 Aug 1332 Battle of Dupplin Moor, Perth, Scotland
William de Irwyn did, in fact, (per "A Short Account of the Family of Irvine of Drum") have a son, William, who WAS married to a daughter of Robert Keith, married to Margaret Hay, who died 17 Oct 1346 Battle of Neville's Cross, Durham, England. This Robert was the grandson of the above Robert .
It might look like this:
........... 9 Sir Robert de Keith
B: Abt 1262 Buchan, Aberdeenshire, Scotland
D: 11 Aug 1332 Battle of Dupplin Moor, Perth, Scotland
........... +Barbara Douglas
B: Abt 1280 Douglas Castle, Douglas, Lanarckshire, Scotland
D: 1350 Castle Cary, Somerset, England
............. 10 Marotte or Mariota de Keith
B: Abt 1300
D: 1335 Drum Castle, Drumoak, Aberdeenshire, Scotland
.............. +William Alexander de Irwyn 1st Laird of Drum
B: Abt 1260 Dumfriesshire, Scotland
D: Abt 1333 Drum Castle, Drumoak, Aberdeenshire, Scotland
............. 10 Sir John Keith
B: Abt 1294 Scotland
D: 1324 Scotland
.............. +?
B:
D:
................ 11 Sir Robert de Keith
B: Abt 1316 Scotland
D: 17 Oct 1346 Battle of Neville's Cross, Durham, England
............... +Margaret Hay
B: Abt 1316 Scotland
D:
................... 12 daughter
.................... +William de Irwyn
B: 1317 Drum Castle, Drumoak, Aberdeenshire, Scotland
D: 1390 Drum Castle, Drumoak, Aberdeenshire, Scotland
The Elizabeth Keith mentioned was the daughter of a totally different Robert Keith (Grand nephew to the adove ........... 9 Sir Robert de Keith)