Why did my opponent get a win when he had only King + Bishop?

I saw a game like that in an OTB tourney thats why I wanted to mention this. Its just not sportsmanlike attitude.

"PS: case #8 has nothing to do with the „new“ rule. This has always been that way, you can try to flag your opponent in non-winnable positions. " @Sarg0n

Although admittedly I have no idea what G.2 is about. Have never heard "We are using the Appendix G" (or not using it) before a tournament.. (similarly, it's rather unclear to me what G.1 means. When does one have infinite time?)

Appendix A applies, A.4c.:
"...the game is drawn if the position is such that the claimant cannot checkmate the player’s king by any possible series of legal moves."

Those mentioned appendices were never valid in blitz.

If Blacked trapped himself with his own pieces, white could've checkmated Black

#14 Yes, these are valid. Appendix B applies to blitz.
B.4 :
"Otherwise, play shall be governed by the Rapidplay Laws as in Article A.4."
Thus A.4 applies to all blitz and rapid play.
Also the newest rules valid from January 1, 2018 contain the same A4 and B4. So these apply to all rapid games, which defined by FIDE is every time control x+y where x+y<60. This covers all bullet, blitz, rapid here at lichess and most of the classical as well.

As far as I can see is „Blitz“ excluded from quickplay finish. III 2.2.

And blitz is defined in Appendix B.

Either way: you cannot have rules online where a referee has to decide draw claims.

So, playing and trying to flag the opponent is normal course. If one agrees to play without increment one should bear the consequences. Especially, in bullet where time is paramount.