Gwent is a
Free To Play Online Collectible Card Game (F2P CCG). As with (almost) every collectible card game, online or otherwise, one of the goals is to collect cards. You do this by buying booster packs. The F2P element is that you can get these booster packs when spending time instead of money. The fact that you can buy boosters and as such buy an advantage means the game is pay to win (P2W) in the strictest sense. However, it's important to note that this applies to the whole F2P CCG genre. So it's pointless to argue whether or not Gwent is P2W. Instead you should compare the game with other CCG and ask how generous Gwent is.
The conclusion is that Gwent is one of the most generous F2P CCG.
So, how can you earn rewards as a F2P player?
1. Daily quest
2. Daily tiers, by winning 6/12/24 rounds
3. GG rewards at the end of the match
4. A leveling system that gives you rewards and unique perks (which, in turn, offers you more rewards)
5. A monthly faction challenge offering extra rewards by completing quests
6. Playing ranked, even at lower ranked you'll receive some rewards at the end of the month
How is Gwent different from Hearthstone and Magic the Gathering, for F2P players?
1. Smaller deck size (making it easier to create competitive decks)
2. You cannot fill your deck with only legendary cards (unlike with HS and MtG, making those decks very expensive)
3. Less frequent expansions with less cards (making it easier to keep up with the collection)
On a final note, for the sake of full disclosure, I have to mention that
Gwent's economy did change when Gwent came out of beta. As a result, premium cards have become more difficult to obtain, but this doesn't affect the gameplay. No refunds for tweaked cards does have some impact, but it's still manageable.