I'm not sure about InfluxDB at all, sorry if I gave that impression. I have however designed and built data architecture for various forecasting software. "all data you perform analytics on is time series data" (from the article) rings so true with me.
However you need to consider that in this sense, it's about what is happening at any given moment in time. In your case, the forecasts are created at a point in time, and that "should" be their index speaking purely from a time-is-the-ultimate-index perspective.
Just some random questions that might help you answer your own questions:
1. Are there multiple forecasts made at the same time, for the same period in the future, but by different systems / algorithms / hyperparameters? Would you not want to keep multiple, and in that regard, what would be the "latest" forecast?
2. If your latest forecast is necessarily the most accurate, why would you need to keep previous versions in the same database?
None of this might be relevant to you, and maybe you'll only get the benefits of InfluxDB by using the forecast time as the index. But I thought I'd give you my thoughts just in case it helps you.