The list of names shown in the OP video was posted by Israel's official Twitter account
So it is true that Israel posted the list displayed in the video. I haven't counted the names yet. It is difficult to tell where one name ends and another begins.
There is a more readable list with ranks here:
356 soldiers and 59 police officers. 10 Shin Bet are also listed, but without rank.
However, this list includes about 37 soldiers killed after October 7th. There is also an official IDF website listing the fallen soldiers.
According to the United Nations Office for the Coordination of Humanitarian Affairs:
The indiscriminate firing of rockets by Palestinian armed groups towards Israeli population centres has continued over the past 24 hours, with no reported fatalities. As of 9 November, the names of 1,162 of fatalities in Israel have been released, including 845 civilians and police officers. Of those whose ages have been provided, 31 are children.
According to the Israeli authorities, 239 people are held captive in Gaza, including Israelis and foreign nationals. Media reports indicate that about 30 of the hostages are children. So far, four civilian hostages have been released by Hamas, and one female Israeli soldier was rescued by Israeli forces. Hamas has claimed that 57 of the hostages had been killed by Israeli airstrikes.
So based on information so far, depending how you consider police and Shin Bet, about 27% were soldiers and 33% were broadly security related.