Cryptocurrency mining entails heavy use of computing hardware (GPUs), which results in electricity costs. Moreover, you're describing the use of the services of a rental business without paying the rent. Consequently, if a scholar would answer this specific question, I would expect them to declare it haram.
The closest fatwa I found describes the use of someone's Wi-Fi without their permission. In this context, a scholar is quoted as saying:
“If we were to determine if it was religiously forbidden or not, we have to look at the privacy and usage laws, and if the extra usage would result in additional expenses for the neighbour.”
But hacking into a secured Wi-Fi account “is not permissible at all. It is like crossing the property rights of others”.
Dubai’s Islamic authority issues fatwa on stealing Wi-Fi, The National
Moreover, the fact that you intend to pay back the gaming station indicates you feel you are gaining possession of something that belongs to them (and hence feel a need to "pay back" something). (And are you paying back the normal rental price of the machines, regardless of whether or not the mining attempt is successful?)
Generally, Muslims are required to obey the "law of the land":
Muslims are generally obliged to abide by the laws of the land and the country they live in...
Many countries have anti-hacking (cybercrime) laws. Let's look at Sri Lanka, which is listed on the OP's profile.
Any person who, intentionally and without lawful
authority causes a computer to perform any function knowing
or having reason to believe that such function will result in
unauthorised modification or damage or potential damage
to any computer or computer system or computer programme
shall be guilty of an offence and shall on conviction be liable
to a fine not exceeding three hundred thousand rupees or to
imprisonment of either description for as term which may
extend to five years or to both such fine and imprisonment.
Computer Crime Act, no. 24, 2007
It's reasonable to conclude the proposed scheme is illegal in Sri Lanka (although, I'm not a lawyer).
Islam discourages deception (see IslamReligion for a survey). There's various ahadith to this effect, such as Allah's Messenger forbade Najsh (Sahih al-Bukhari 2142).
A vigilant administrator would detect the heavy use of these machines during idle time, and take action against it.