Is De-mat account 'compulsory' even if I want to do intra-day trade only?

No, Demat is not necessary for intraday trades in Equity.

Also if you are trading in F&O then you don’t need dmat account for even positional trades.

Demat is required for taking delivery positions in Equities only!

Even though demat is not required for intraday trading, exchange has made it mandatory that all trading accounts who wish to trade intraday equity should mandatorily have some demat account mapped to the trading account. The reason for this is if assuming an intraday stock hits circuit down, forcibly delivery has to be taken, and there has to be some demat mapped to take this delivery.