- Is this an error? Is it slang? Does it sound OK to native speakers?
Let's remove the extraneous material from the sentence:
- The presenter baffled viewers by remaining to wear her wedding ring.
This is comprehensible, but it isn't idiomatic unless the reporter was trying to say that the presenter remained on stage after the performance in order to wear (put on) her wedding ring.
- What should the author have written?
The word continuing conveys the notion that conveys the sense you describe:
1.2 Remain in a specified position or state.
- The presenter baffled viewers by continuing to wear her wedding ring.
- What rule of grammar is this construction breaking? If any?
Consider the example given in the following definition:
1.2 [with complement] Continue to possess a particular quality or fulfil a particular role.
‘he had remained alert the whole time’
It is conceivable that the reporter was thinking of this usage. The following might be acceptable:
- Even after all that, she remained wearing her wedding ring.
It has a nostalgic sense as something about a woman who has been left behind but still holds the symbol of marriage dear.
However, your quote doesn't appear to have this connotation, leading to the remained-on-stage reading vying with the nostalgic sense. The result, strangely, sounds odd but still makes sense.
- Is this an example of contemporary English?
Ngram doesn't appear to have any instances of "remaining to wear", but it only reports up to 2008, so there may be more recent instances that remain unreported.
Looking at the first page returned by a google search for "remaining to wear" (with quotes), we get several examples like the following, which is a different construction to your quote:
- Hopefully after you have decluttered you will have enough clothing remaining to wear and there will be no need to add to this for some time.
Only one of the examples fits the construction of your quote; it is dated May 28 2014, so can be considered contemporary:
- Ghost skills allow you to obtain low detection while remaining to wear heavier armors or weapons and still be able to participate in stealth aspects of the heist.
As noted by @StarWeaver and @TRomano in comments, this site contains other instances of non-idiomatic usage. The STEAM quote cited is in English and it is contemporary, but it might be a stretch to call it Contemporary English as used by the wider community of native English speakers.
Note that your quote features on several of the links returned on the first page. One of them is a variant of the page you linked to. Its headline includes the following words, agreeing with my suggestion above to use continuing instead of remaining: