Nah, don't worry.
Yes, voting on users rather than posts is generally a bad approach to SE. You ought to consider the content of the post, not who wrote it. But going as far as saying some dude encouraging people to give feedback on their posts in his profile text is actively violating this might be...taking it a little too far.
Maybe think twice about voting up something just because your best friend wrote it or downvoting that answer from this dude who left this rude comment on your question. But let's try to not lose sight of the forest for the trees. There can sometimes be a thin line between stumbling over an avid new user's interesting answers and...going on a hunt to upvote someone's stuff. The same way someone asking you for honest feedback on their answers could be construed as an underhanded vote-beg, but...it really doesn't need to.
In general, I'd be hesitant to judge all kinds of advertizement people do for their posts as "begging for rep". In fact, I've made the experience that pessimistic approaches like that often point to too much of a score-minded approach to SE in the person uttering the complaints. This isn't to say this necessarily is the case here and your honest concern is still appreciated. But I've seen site cultures where too much of a concentration on reputation and competitiveness has grown into a general distrust of any other motivation for e.g. advertizing an interesting post in chat or posting a self-answer and things like that. For example when you say stuff like "there would need to be 5x as many negative votes as positive votes for this not to be a net positive in user rep" this seems like a lot more elaborate considerations than what the user of that profile link put into it themselves. ;-)
On the bottom line, yes, you can take this as begging for votes, but that is by far not the only interpretation, especially not in the way it is written. And in this way it seems totally harmless in a profile about me section, especially since this is also the singlemost place where you have the most freedom for expression on SE (still under some restrictions, though). It's not even uncommon for people to share a list of their coolest SE questions in this section.