A right of first refusal is the right to purchase the shares offered by a company to someone else. So if VentureBros wanted to invest $10M in TheGuild, and TheGuild's old VC, ImpossibleIndustries, had a ROFR, ImpossibleIndustries could block VentureBros and buy the same shares for $10M.

Pro-rata participation rights means that if you sell shares to a third party, the rightsholder gets to purchase more stock from the company in order to maintain their percentage share so that they are not diluted. So if ImpossibleIndustries owned 10% of TheGuild, and VentureBros then invested $10M and got a certain percentage of TheGuild, ImpossibleIndustries would have the right to buy more stock of TheGuild in order to ensure that, after the transaction, ImpossibleIndustries still had 10% of the total shares of the TheGuild.

Pro rata is just ROFR with a 1x multiple, yes, so it seems it was the particular multiple (anything greater than strictly proportional) that was onerous.