Who was Wales founded by?

Assuming you mean the WRU and not the country then it was the selection of the first official Welsh team by the remarkable Richard Mullock to face England at Mr Richardson's Field, Blackheath on 19th February 1881, that hastened the formation of what we now know as the Welsh Rugby Union.
The WRU have been the head administrators of Wales's national sport since 1881. A group of 11 clubs - Swansea, Lampeter, Llandeilo, Cardiff, Newport, Llanelli, Merthyr Tydfil, Llandovery, Brecon, Pontypool and Bangor - came together at the Castle Hotel, Neath on 12th March 1881, to form the Welsh Rugby Football Union. It was a meeting that took place on the same day that Cardiff beat Llanelli in the fourth South Wales Challenge Cup Final in Neath.
Cyril Chambers, of Swansea Football Club, was elected the first President of the WRFU and Richard Mullock, of Newport, became the first Honorary Secretary and Treasurer. It had been Mullock who had selected the Welsh team to play in that first, fateful international at Blackheath against an England side that had being playing internationally for a full decade and that had lost only twice in their 17 Tests to that time.