If the SSJ is a x10, then this is the only possibility. ButThere was a point where I was reading the Viz translation and started piecing it together that maybe the "x2, x3, etc." referred to the Kaio-ken itself, not Goku's power
[spoiler]
[/spoiler]"カラダじゅうのすべての気をコントロールして瞬間的に増幅させるんだ
うまくいけば力もスピードも破壊力も防御力もぜんぶなん倍にもなる"
"Control all the Ki running through the body and amplify it instantly!
With luck, strength, speed, destructrive force and defensive force, everything is multiplied."
In fact, he literally says "make it instantly amplify" (speaking of the Ki).
So Kaioken = amplification of the Ki => multiplication of the combat force.
(You will notice that using the kaioken, Goku inevitably amplifies his Ki reserve, but that what makes up the fighting force is not sure to be multiplied ("with luck, everything is multiplied"). And the effect is necessarily degressive, proportional to the quantity of Ki that it manages to control.
Let us now return to the passage of Tenshinhan.
[spoiler]
[/spoiler]"You would not forget the regular Kaioken?
If we talk about the Goku now, he can endure the power by about 10 times." (the power of the Kaioken)
A few pages later, we have Tenshinhan who specifies it:
[spoiler]
[/spoiler]ででは孫のやつはすでに限界である10倍の界王拳を使っていながらやられちまってるってことですか...?
You mean that Son takes a correction while he is already using the Kaioken of 10 times which is the limit."
Juubai no kaioken
Conclusion: When Tenshinhan spoke of a power multiplied by 10 (power of 10 times), it is indeed Kaioken that he spoke.