No, the speed of light is not mentioned in the Qur'an. There is no evidence that points to any such conclusion. The tafsīr of the verse you quoted (Surat As-Sajdah 32:5) has been covered by many scholars from the salaf (times close to the Prophet's) and the khalaf (modern times).
In his tafsīr, Ahmed ibn Mustafa al-Maraghi said:
والمراد بالألف الزمن المتطاول، وليس المقصد منه حقيقة العدد، إذ هو عند العرب منتهى المراتب العددية، وأقصى غاياتها، وليس هناك مرتبة فوقه إلا ما يتفرع منه من عداد مراتبها
What is meant by "a thousand years" is extended time; it is not meant to be an exact number since for the Arabs, one thousand is the highest number they used, with nothing above it apart from its multiples.
You will indeed find that Arabs at the time used a thousand-thousand to denote one million, for instance. In another modern tafsīr by Ibrahim al-Qattan, he mentioned the same concept saying that a thousand years denoted a long period of time (not an exact number), then added that a day could be much longer than that.
In his tafsīr, Al-Mawardi said that "a thousand years" could mean one of three things:
- Allah ordained in one day the matters of a thousand years, then He would pass this to His angels. When a thousand years have elapsed, Allah would ordain in one day the matters of another thousand years, and so on. This is what Mujahid said.
- Angels take a thousand years to descend and another thousand years to ascend, and this is what Ibn 'Abbas and Ad-Dahhak said. According to them, the first sky was separated from Earth by a thousand years of travel.
- Angels take a thousand years to ascend and descend (hence, 500 years each way), and this is what Qatada and As-Suddi said.
Al-Qurtubi in his tafsīr said that the day which is "a thousand years" equivalent is the Day of Judgment.
None of the scholars explained this verse in any form to indicate a relation to the speed of light. In addition, all the links that were referenced in the post you mentioned leave a lot to be desired from a mathematical or logical point of view.