Deep Learning based time series forecasting According to the paper "Statistical and Machine Learning forecasting methods: Concerns and ways forward", it looks like the recent DNN-based approach has weaker predictive power in extrapolation, i.e. time series forecasting than statistical algorithm like VAR or ARIMA. 
The benchmark result is contrary to the current Deep-Learning-beats-it-all trend. Is the reason behind the result from the fact that DNN algorithms require a large-sized data?
 A: You can't meaningfully talk about DNNs or ARIMA being "better at time series forecasting". It depends enormously on what kind of series you are looking at: short vs. long series, many vs. few or only one related series, causal drivers or not etc.
Anyone who makes sweeping statements here is like a salesman who knows exactly what kind of car you need - without bothering to find out whether you need to drive offroad, commute two miles to work, need to move a Little League baseball team, or want to transport cattle.
As a very rough rule of thumb, classical methods perform competitively if you have few short series. DNNs may work better if you have many related series. (It depends heavily on whether the person setting them up knows what she or he is doing.)
A: You might also consider the drivers behind 'Deep-learning-beats-all' trend you mention. Much of the hype around these techniques comes from the superiority of these methods in image recognition and natural language problems. These domains are defined by exceptionally large datasets (e.g. ImageNet > 14 million images, it's possible to find very large text corpora). So just by understanding why these methods are popular in the first place more or less answers why they are less used for time series (since time series datasets are much smaller).
As an example of how short important time series datasets can be very small consider that if you wanted to model US GDP, the Federal Reserve has quarterly data going back to 1929, which is only about 360 datapoints!
A: 
Is the reason behind the result from the fact that DNN algorithms require a large-sized data?

There are parallels to time-series and tabular data. A recent work Tabular Data: Deep Learning is Not All You Need shows similar trends that DNN does not out perform conventional models on tabular data. However, it is right that the learning capacity of DNNs are advantageous when there are very large datasets. More justice to deep learning would be to say this is an open research area and DNNs have great potential over conventional time-series models.
PS: To give link to paper Statistical and Machine Learning forecasting methods: Concerns and ways forward lead by Cypriot researcher
A: Statitical tools applied to time series forecasting are very developed and approach-oriented methods. You find many technics arima sarima sarimax var varimax vecm.... And each method had been developed  for a particular situation and type of data and serie.
In the other hand DNN such as RNN, LSTM.. Are challenging models that have not been very used in this field, so haven't experienced many situation so they can been evaluated and updated in a large scale.
I had the chance to work for a system of medels, combined, for a platform that forecast time series of eco, demo, social... Indicators and it happen that sometimes LSTM get a better result.
What I can claim is that DNN are not good when it comes to random trend chocs.
