If you are using VPN for anything other than committing a crime, then there's no problem as per the law.
Long answer with personal opinions
This law which was announced January, 2016 is mainly targeting criminal activities including cyber crimes and VoIP calls. It also acts as a scarecrow for the general public.
For normal people who are seeking porn or other silly blocked content, no one will bother to prosecute them. I have many friends there and I have personally used proxies there and nothing ever happened, but I wasn't doing any "criminal" activities.
I have spent time reading the UAE law regarding this, it's not clear and it's vague. I believe it will be used only against terrorists, or against people who sell VoIP calls in bulk.
In addition to the above, one of the official newspaper in the UAE (in Arabic) quotes parts of the actual law, which I could not find in English, states the following (rough translation):
... A fine of 2,000,000 AED or prison to those who use techniques to get a false IP address with the intention of committing a crime..
This is the only piece of the new law I was able to get online, and it clearly is vague, and it also mentions "the intention of committing a crime", which confirms what I said earlier, it's not meant for the general public and their use of VPN to watch porn or something.
Some other newspapers have articles about an interview with an official in Dubai police, who clearly was talking about criminals, such as terrorists, blackmailers, etc.