No. You aren't required to subscribe to Xbox Live Gold to have a great Xbox gaming experience. While it offers features such as multiplayer gaming, free games, game discounts, accessories discounts, and others, you might not find them as appealing if you prefer to play on your own with specific titles.
However, subscribing is still a good option if you want to expand your Xbox game library with free and exclusive content, as you can get discounts on additional games when you have a subscription.