Candidly speaking, that alien could be anywhere in terms of power; however, if he sat in the same realm of strength as one of the strongest elite fighting forces in the universe, he likely would have attracted some attention.
It's not like Freeza's empire covered the entire universe or anything -- it certainly didn't by the time Beerus woke up, anyway, considering that without Freeza himself to lead it his army hadn't been doing so well. Heck, we already saw one example of a planet Freeza hadn't already conquered which was home to a Ginyu Force level fighter -- Namek, with Nail being on or above the level of Recoome and company. So it's entirely possible that some random alien on a middle-of-nowhere world that nobody even bothered to investigate could be on par with the Ginyu Force and nobody would ever know -- being Super Saiyan level is another matter of course, and he's certainly not SSj3 level or random people in the afterlife would be sensing him, but I don't see anything wrong with some of the strongest random alien fighters being as strong as or stronger than the Ginyu Force. I mean, that's literally the exact backstory of each Ginyu Force member -- they're super-strong mutants compared to the rest of their kind.
Heck, it's entirely possible that there's random aliens out there who are starting to approach the 1,000,000 mark, or at least surpass the 530,000 level that first-form Freeza had. Doesn't Freeza describe his
third form as the one that nobody's ever seen before -- which would mean that someone he fought previously was strong enough to make him use his second form?
But yeah -- the alien Beerus fought could be pretty much anywhere in the pre-Super Saiyan levels of power, from Raditz-ish all the way up to the low single-digit millions, without contradicting anything or causing problems with other statements. It's pretty much impossible to even guess an exact power level, or even a range that isn't super broad, with any accuracy. Relying on stuff like fire and electricity kind of makes me think he's probably not all that strong, though -- like maybe somewhere in the lower Saiyan Saga range at best. I don't think attacks like that would be all that effective compared to regular ki blasts beyond that point, unless they're magic-based (not just "normal" fire) like Dabura's fireballs.
