What's worse, not resigning when lost, or continually offering draw when lost

Obviously the latter, although I'm pretty sure it was a rhetorical question.

You can't be penalized for the former, but you can for the latter.

18 moves in and 2 pawns up does not mean a certain win. Maybe young Oliver thinks that he has good chances.

But if he stops moving and keeps asking for a draw, I could get a bit peeved myself

just decline the first offer (or move) and ignore repeated offers. some people do it just to get your goat which obviously worked here in this example. the only difference now is that it has become the subject of public discussion which is rewarding silly behavior with unwarranted attention. file a complaint with chess.com and stop trying to name and shame. he obviously doesn't care.

One insults the intelligence of someone who probably doesn't know how to mate while the other breaks the rules.

Maybe the player isn't insulting his or her opponent by not resigning like if my opponent has a forced mate in 10 moves and they played really,really well I won't tip the King I'll let them play it out to the finish I want them to show me they see the mate and can do it perfectly without mistakes.

When it's a very beautiful finish both players are winners no matter who won.

Well, it's not really an insult if the player is testing skills not yet possessed, even though some posers get their knickers in a twist. I get a lot of draws and even occasional wins on time in blitz because my opponents lack elementary checkmate skills even after outplaying me in the opening and/or middlegame. I've seen players spend fifteen seconds and as many moves trying to finish a win after missing an elementary mate in two.

By far it's continually offering a draw when losing badly.  Not only is it vexing, but it's poor sportsmanship.  If you play on a little and you're playing a player rated under 1800 there is at least a chance a human will blunder.  In any event just finish him if he plays on.  It's his right to do that.  No one said you have to resign.  There can be too much resigning in chess.  But offering stupid draws, well...