It is his time to waste it, and it is your job to prove the advantage. Offering a draw in losing position like that is dubious, for sure. If you were blocking him for that reason, I would understand. Your reasoning, however, is a bit unreasonable, in my humble opinion, as what he did isn't bad at all. It can make a player more resourceful, especially when they are lower rated. I will state my case below.
I just know that I would be a lot worse today if I resigned at the first sign that I am losing the game. Not only that I have drawn and even won some of that games, but there is a secondary, much more important reason why you shouldn't be mad at someone because they are not resigning early. You would have less experience in endgames, you are less resourceful because you can't find tricky moves etc. if not playing out some bad positions. You don't have to play till mate, but at least for some time, and even till mate if you have the will at lower levels.
There was a game, I had a queen vs a knight endgame, it is completely winning but at that time, I am sure I didn't know how to win (I know now, but I could still mess it up because I had it only once on the board). My opponent just resigned without question, after about 5 seconds in an 1 hour per side game. On the other hand, I sacrificed a piece for opponent's last pawn and played out knight and bishop vs my lone king, and of course he didn't know how to win it, I still don't know that checkmate.
Learning tricks, stalemate tricks, perpetual checks etc. , is not just important for losing positions, it transposes to other areas of the game.
If you are here just for fun, and don't care about improvement, that is valid, but if that is the case, why writing this post in the first place?
I would say that you would like to better your game. If that is the case, this is not really the way to do so. But of course, you may do as you wish. If not something else, I am giving you the opportunity to block me right now and not be frustrated in the future if some algorithm decides for us to play a game, as you know my stance on resignation.
I play here for fun (and only very distantly secondarily, for improvement). I do play chess in other places for improvement. And whereas I'll always morally disapprove of not resigning, I'm ok with it in official competitions or when I know it's the player's philosophy and I voluntarily enter the game.
One of the things that blitz chess (especially over the Internet) has amped has been the rise of the non resigner mentality, the flagging mentality, the traps in the opening mentality. Even titled players who I like a lot have flirted or even downright espoused those philosophies. Paired with young people for whom winning at all costs comes naturally, the gentlemanly essence of the game is being lost at an accelerated pace. That's my take. And my very very very modest attempt to bring back manners by disengaging with people who go for that degeneration is what feels right to me.
I'll concede that its difficult to determine what's considered a losing position is all dependent on the strength of the player among other things.
No, it's not wrong not to resign a game. You have the right to play on until checkmate, stalemate, draw by repetition or agreement or even draw by arbiter's decision (in tournament games). You do whatever you want within the rules. And the rules don't mandate resignation at any time.
My point is about etiquette and the way I see sportsmanlike conduct. You are free to disagree. You even have GMs like Serper in this very website supporting the "never resign" philosophy. I... just disagree. If someone doesn't resign a lost position and even offers a draw in it, my MO so far has been to ask why. If I get a "I never resign" response, I'm likely to block them. It's my right too