Unfortunately, no. The above vids are for the ps2 SRW Original Gaiden.
There are 4 SRW games available in English. 3 of them GBA and 1 of them PS1. SRW Original Generation 1 & 2 for the GBA have been officially released outside of Japan, SRW Judgement(gba), and Alpha Gaiden(PS1) have been translated 100% by fans.
The reason why is because the SRW games feature characters from all kinds of different anime series, like a big party, and you know how Japan is in terms of licensing. OG 1 & 2 were released outside Japan because it featured ONLY Banpresto Originals so there were no licensing issues... There are still many many maaany translation projects ongoing though.
I'd totally recommend the PS1 version to you, as you can, well technically, play it on PC 100% English, that's all I can say right here, you know? The translation isn't illegal, though. Afaik.
Believe me, if the SRW games, be it ps2 or p3, would be released outside of Japan it would be enough for me to run to the store and throw my money over the clerk's head. TAKE IT!
The SRW games keep incorporating small new features in every game, but it stays exactly the same in how it works. So because I've now played 4 of them in full Enlish I could easily make my way through a Japanese version, I just wouldn't know what the characters are saying most of them time. Note that there is almost always a Story Translation Faq available if you don't mind playing first and reading later. It's a bit of a drag but it's really the only way.
Ps: Sorry for the long story.