Say I bet on something, but the prize for winning is points instead of cash that you were freely given daily. You can also buy more points if you want to play more, but it is not required. However, you could use these earned points to buy coupons or gift cards. Would this be considered gambling under law?
Yes, this is gambling.
The coupons have a value; gambling is the wagering of something of value.
As to if it is illegal gambling, that would depend on the law in the jurisdiction where it takes place: for an internet transaction this could be the jurisdiction of the website owner or the user or both.
As an example: in Australia, the Interactive Gambling Act 2001 is administered by the Department of Communication and the Arts, it provides:
Any game of chance, including games of mixed chance and skill played over the internet, is prohibited under the Interactive Gambling Act 2001 if it’s provided to someone who is physically in Australia.
The Act defines a gambling service as:
gambling service means:
(a) a service for the placing, making, receiving or acceptance of bets; or
(b) a service the sole or dominant purpose of which is to introduce individuals who wish to make or place bets to individuals who are willing to receive or accept those bets; or
(c) a service for the conduct of a lottery; or
(d) a service for the supply of lottery tickets; or
(e) a service for the conduct of a game, where:
(i) the game is played for money or anything else of value; and
(ii) the game is a game of chance or of mixed chance and skill; and
(iii) a customer of the service gives or agrees to give consideration to play or enter the game; or
(f) a gambling service (within the ordinary meaning of that expression) that is not covered by any of the above paragraphs.
The Act provides exemptions, however, based on the small amount of information in your question its hard to tell if any would apply. Broadly, the exemptions allow for certain types of gaming to be licensed/regulated.
The Act applies to any service that may be accessed by people in Australia irrespective of where it is in the world.