Yes, you have to pay the strike price when exercising.
So what does a trading price of the warrant at $0.60 now mean?
It means that the buyer expects the stock price to go above $4.85 ($4.25+$0.60) within the next 5 years…and/or the stock price will increase thereby causing the warrant to increase (by the math above) and they will be able to sell for a profit.
Since very few of the warrants will be exercised in the next 3-4 years, it is primarily a speculative investment derivative of the common stock price.