Did they reach space?
The Virgin Galactic SpaceShipTwo class craft "VS Unity" flew Branson up to 53.5 miles (86 kilometres). This altitude is considered "space" by the US air force, and nobody else. It is above most of the atmosphere, and does provide a nice view of the Earth.
The Blue Origin New Shepard class craft "RSS First Step" flew Bezos up to 107.05 km. This is considered "space" by the whole world, but most relevantly by the FAI (
Fédération Aéronautique Internationale), which is the globally acknowledged body that governs records in aeronautics and space. This altitude is over the Kármán line at 100km, which is the accepted altitude where space begins.
But did they really go to space?
Sort of. They both flew suborbital hops, neither vehicle is designed to even attempt to achieve orbit.
Do these events carry serious implications for astronautics
Sort of. The BO New Shepard rocket has been used multiple times to perform very shortduration experiments in space. However this is nothing new as mankind has been launching suborbital, Kármán line crossing sounding rockets since the early 1940's. The New Shepard does provide a very gentle recovery ability which very few if any sounding rockets can provide, and provides a much more benign environment on the launch too, avoiding the punishing accelerations and vibrations common with smaller rockets.
So what is the primary purpose of these flights?
And tourism! They are selling tickets for flights on these vehicles for several hundred thousand dollars a seat, and people are queuing to buy them.